Quiz 5.1 Review!

Right Angle Trig

100

Given ∠A = 30º, opposite = 7, what is the hypotenuse = ?

Hypotenuse = 14

200

Given ∠B = 45º, adjacent = 12 , what is the opposite = ?

Opposite = 12

300

From the top of a 180-ft cliff, the angle of depression of a ship is 28°. Find the distance from the ship to the base of the cliff.

Distance ≈ 339 ft

400

Marcus is 70 inches tall. If the angle of elevation of the sun is 35°, how long is his shadow?

Shadow ≈ 99.9 inches

500

A building is 60 m tall. The angle of elevation from Sarah to the top of the building is 25°. The angle of elevation from Luke to the top of the building is 55°. Both are on the same side of the building. What is the distance between Sarah and Luke?

Distance between Sarah and Luke ≈ 74.9 m

Number of Solutions

100

Determine how many solutions the triangle has. DO NOT SOLVE. A=35º, a=20, b=28

2 solutions

200

Determine how many solutions the triangle has. DO NOT SOLVE. A=40º, a=30, b=20

1 solution

300

Determine how many solutions the triangle has. DO NOT SOLVE. A=120º, a=15, b=22

0 solutions

400

Determine how many solutions the triangle has. DO NOT SOLVE. A=50º, a=10, b=16

0 solutions

500

Determine how many solutions the triangle has. DO NOT SOLVE. A=25º, a=18, b=30

2 solutions

Law of Sines/Cosines

100

In △ABC, A = 30º, a = 10 , B = 45º. Find b.

b ≈ 14.1

200

In △GHI, G = 40º, H = 65º, g = 15. Find h using Law of Cosines.

h ≈ 21.2

300

In △DEF, d = 12 , f = 18, E = 50º. Find ∠F.

No solution

400

In △JKL, j = 14, k = 18, l = 20. Find ∠J.

J ≈ 42.7º

500

In △MNO, m = 25, n = 30, o = 40. Find all angles.

M ≈ 38.6º, N ≈ 48.5º, O ≈ 92.9º

Solve Triangles

100

In △XYZ, base =10 cm, height = 6. Find the area.

Area = 30 cm²

200

Solve the triangle: A=97º, C=42º, c=12

B = 41.0º

a = 17.8

b = 11.8

300

Solve the triangle: 

a=9, b=7, c=12

A = 48.2º

B = 35.8º

C = 96.0º

400

Solve the triangle:

B=48º, c=18, a=14

b = 13.5

A = 50.3º

C = 81.7º

500

Solve the triangle: A=42º, a=12, b=14

Solution 1

• B = 51.4º

• C = 86.6º

• c = 17.9

Solution 2

• B = 128.6º

• C = 9.4º

• c = 2.9

Area of a Triangle

100

In △ABC, b=8 cm, c=12 cm, m∠A=40º. Find the area of the triangle.

Area ≈ 30.9 cm²

200

In △DEF, d=15 m, e=20 m, m∠F=72º. Find the area of the triangle.

Area ≈ 142.7 m²

300

In △ABC, a=8 cm, b=10 cm, c=12. Find the area of the triangle.

Area ≈ 39.7 cm²

400

In △GHI, g=10 ft, h=14 ft, m∠I=35º. Find the area of the triangle.

Area ≈ 40.2 ft²

500

In △XYZ, x=11 m, z=10 m, m∠X=95º. Find the area of the triangle.

Area ≈ 18.8 m²