Question

Juwan stood 14 feet away from a spot directly underneath a bird's nest and looked up at the nest with an angle of elevation of 36°. Juwan's eyes were 5 feet from the ground. Enter the height of the bird's nest above the ground, rounded to the nearest foot.

Answer 1

Answer: The height of the bird's nest above the ground is 15 feet

Explanation:

Extracting key information from the question:-

*** Juwan stood 14 feet away from just under the nest.

*** He looked at the nest with an angle of elevation of 36°.

*** His eyes were 5 feet from the ground.

Now, the shape that is created in this situation is a righ-angle triangle. In order to calculate the height of the bird's nest above the ground, we will need to apply Sohcahtoa rule in order to find "x"(which is the height of the bird's nest from 5 feet above the ground).

Opposite/adjacent = tan B°

Where opposite in this case is "x", the adjacent in this case is 14 feet while B = 36°

Applying all these in the formula:-

(x/14) = tan 36°

x × 1 = 14 × tan 36°

x = 14 × 0.7265

x = 10.171

Now, to calculate the height of the bird's nest from directly above the ground, we must then add the calculated "x" and the distance or height of Juwan's eyes from above the ground (5 ft)

This is :

10.171 + 5

= 15.171

= 15 feet (rounded to the nearest foot)

Answer 2

15 feet

Explanation:

I\

X I \

I__\

X+5 I___\

14ft

tan∅ = opposite / adjacent

tan(36°) = x / 14

therefore X = tan(36°) * 14

X = 10.172

And juwan's eyes was 5ft above the ground level

therefore, the height of the bird's nest above the ground level will be

= X + 5 = 10.172 + 5

= 15.172 to the nearest foot

= 15 ft