Solve the triangle. Round decimal answers to the nearest tenth. ​

Answer:

x = 5.7           y = 9.4

m∠H = 31°

Step-by-step explanation:

cos of an angle = adjacent side/hypotenuse

and sine of an angle = opposite side/hypotenuse

cos 59 = x/11          and sin 59 = y/11

11 cos 59 = x                  11 sin 59 = y

x = 5.7                             y = 9.4

m∠H = 90 - 59 = 31°

You need  to memorize the definitions of all the trig functions and then these types of problems will be easy for you.

[tex]x=5.7[/tex], [tex]y=9.4[/tex]  and ∠[tex]H[/tex][tex]=31[/tex]° is the solution of the triangle.

What is trigonometric ratio?

Trigonometric ratios are the ratios of the length of sides of a triangle. These ratios in trigonometry relate the ratio of sides of a right triangle to the respective angle.

The basic trigonometric ratios formulas are given below :

sin θ = Perpendicular/Hypotenuse

cos θ = Base/Hypotenuse

tan θ = Perpendicular/Base

sec θ = Hypotenuse/Base

cosec θ = Hypotenuse/Perpendicular

cot θ = Base/Perpendicular

The sum of angles of a triangle equals the straight angle (180 degrees, π radians, two right angles, or a half-turn)

According to question,

In Δ FGH ,

∠G = 59°

Hypotenuse of triangle = 11

Base of triangle according to the ∠G = x

Perpendicular of triangle according to the ∠G = y

Now,

Cosθ =  [tex]\frac{Base}{Hypotenuse}[/tex]

[tex]Cos[/tex] 59° =  [tex]\frac{x}{11}[/tex]

   [tex]x[/tex] [tex]=11[/tex]× [tex]0.515[/tex]     (  Cos59° = [tex]0.515[/tex] )

     x [tex]=5.7[/tex]

Sinθ = [tex]\frac{Perpendicular}{Hypotenuse}[/tex]

[tex]Sin[/tex] [tex]59[/tex]° [tex]=\frac{y}{11}[/tex]

      [tex]y=11[/tex] * 0.857

       y [tex]=9.4[/tex]

According to the sum of angle of triangle

∠F + ∠G +∠H = 180°

90° + 59° + ∠H = 180°

∠H = 180° - 90 -59

∠H = 31°

Hence,[tex]x=5.7[/tex], [tex]y=9.4[/tex]  and ∠[tex]H[/tex][tex]=31[/tex]° is the solution of the triangle.

Learn more about trigonometric ratio and sum of angle of triangle here:

https://brainly.com/question/8711345

#SPJ2

PLSSSSS HELP MEEEE PLSSSSSSS


Thelma and Louise ordered take-out from Belle Taco. Thelma ordered 2 tacos and 1 burrito and paid $3.79. Louise ordered 2 burritos and 1 taco and paid $4.58..


Find the cost for 1 of each of these items.

Which of the following statements is NOT a property of parallelograms?
Opposite angles are congruent.
Opposite sides are parallel.
Parallelograms have 4 straight sides.
All sides are parallel.

Hurry, it’s a test!!! Plz!
Raj estimated the sum of 214.73 and 9.6 by rounding each number to the nearest whole.
What was Raj's estimate and what is the actual sum of the numbers?
Enter your answers in the boxes.
Raj estimated the sum to be [ ]
The actual sum is [ ]

PLS HELP 30 PTS!!!Use the coordinate plane to help you identify the length of each leg then use the Pythagorean Theorem to find the length of CD

Type your answer in the box.

Note: Type in only numeric part of the answer. Round your answer to the nearest hundredth.

Example: 12.70

Which expression below has the same value as 9⁶ ?

9 • 6

96

9 • 9 • 9 • 9 • 9 • 9

6 • 6 • 6 • 6 • 6 • 6 • 6 • 6 • 6

The highest point in Chicago is 735 feet above sea level. You can represent that numerically using .

Samples of size 60 are drawn from a large population known to have a mean of 78 and a standard deviation of 12. What proportion of these samples would we expect to have a mean greater than 80?
a
0.566
b
0.098
c
Almost none
d
0.434
e
0.901

Susan Carver will purchase a home for ​$190000. She will use a down payment of ​18% and finance the remaining portion at ​4.2%, compounded monthly for 30 years

The hospital is putting in a wheelchair ramp at one of its entrances. Only 6 feet of sidewalk can be covered by the ramp, and the ramp needs to reach 0.5 feet up the wall to reach the entrance. How long does the ramp need to be?

how do you solve 3 divided by x -1 = x + 1

Joel spent $28 for an Internet data service
and
pays $14.50 per month. He spent 24 50 to join
an online movie streaming site and bays $13.25
per month. Write an expression to represent
Joel's total cost for both memberships after
m months

The range for the set of data represented by the following box-and-whisker plot is 8.

Square root of 9 + square root of 64?

Write a proportion for brainliest

Me han descontado 10 euros en unos pantalones que estaban rebajados un 20 porciento .¿cuantos costaban los pantalones ?¿cuanto ha pagado por ellos ?

E = MV^2 ÷ 2 + mgh, If M=20, h=15, E=4900, g=9.8. Find V​

Simplify the following
√2+√3/3√2-2√3​

An airplane is flying at a constant speed. The airplane descends 450 meters in 9 seconds. Write the speed of the airplane as an integer.

Calculate the result of operations, round the result to the tenth

5/2 + √2

5(x + 8) + x + y, given that x = 3 and y = 30

Exercice 1:
Voici un programme de calcul :
Choisir un nombre
Multiplier ce nombre par 4
Ajouter 8
Multiplier le résultat par 2
1. Vérifier que si on choisit le nombre -0,5, ce programme donne 12 comme résultat final.
2. Le programme donne 34 comme résultat final, quel est le nombre choisi au départ ?
Dans la suite de l'exercice, on nomme x le nombre choisi au départ.
3. L'expression A = 2(4x + 8) donne le résultat du programme de calcul précédent pour un nombre x
donné.
On pose B = (4 + x)2 – x2
Prouver que les expressions A et B sont égales pour toutes les valeurs de x.
4. Pour chacune des affirmations suivantes, indiquer si elle est vraie ou fausse.
On rappelle que les réponses doivent être justifiées.
Affirmation 1: Ce programme donne un résultat positif pour toutes les valeurs de x.
Affirmation 2 : Si le nombre x choisi est un nombre entier, le résultat obtenu est un multiple de 8.​

find the measure for angle A

Jim rides the bus to and from school each day. A one-way trip is 8.12 kilometers. How many kilometers does he travel in 3 days?

The value of an antique car is modeled by the function V\left(t\right)=10700\ \left(1.125\right)^t , where t is the number of years since 2005.

By what percent rate is the value of the car increasing per year?

a
125%
b
12.5%
c
1.125%
d
0.125%

You purchase five municipal bonds on the first of the year. The current market value price is [tex]101\frac{1}{4}[/tex]. The commission charge is $8 per bond. What is the cost of purchasing these bonds?


a.$5546.25
b.$5102.50
c.$5062.50
d.$546.25

Jackson has scores of 80, 90, 83, and 81 on four Math quizzes. What is the score he needs on the next quiz to achieve an average above 85?​

Daniel's school is selling tickets to a choral performance. On the first day of ticket sales the
school sold 1 adult ticket and 3 child tickets for a total of $39. The school took in $87 on the
second day by selling 5 adult tickets and 3 child tickets. Find the price of an adult ticket and the
price of a child ticket.

What is the measure of Angles are not necessarily drawn to scale.

What is the value of x?

Jess make a big kettle of rice and beans.He used 1 1/2 cup of beans he used 4 cups times as much rice how many cup of rice did Jess use​