Question

A surveyor found the angle of elevation from the ground to the top of the building at two locations 20 feet apart as shown below.
Which measurements are correct? Round side lengths to the nearest hundredth. Check all that apply.
m∠A = 57°
m∠B = 15°
c ≈ 10.89 ft
h ≈ 8.09 ft
h ≈ 31.28 ft

Answer 1

Answer:

Option B and Option E are correct.

Step-by-step explanation:

A surveyor found the angle of elevation from the ground to the top from a point = 33°

Then moves 20 ft towards the building angle of elevation becomes 48°.

Now as per figure attached

m∠A + 48° = 180°

m∠A = 180 - 48 = 132° [∠A and 48° are supplementary to each other]

m∠B + 33° + 132° = 180°

m∠B = 180 - 165° = 15°

$\frac{sin33}{c}=\frac{sinB}{20}$ [sine rule]

$\frac{0.5446}{c}=\frac{sin15}{20}=\frac{0.2588}{20}=0.0129$

$c=\frac{0.5446}{.0129}=42.22$

Now $sin48=0.7431=\frac{h}{c}=\frac{h}{42.22}$

h = 0.7431×42.22 ≈ 31.28 ft

Therefore Option B and Option E are correct.

Answer 2

The second and last one are right