Question

question 20
1 pts
the angle of elevation from a point on the ground to the top of a
building is 35 degrees. if the point on the ground is 150 ft from the
building, how tall is the building?
254 feet
105 feet
183 feet
212 feet
question 21
1 pts
a boat is spotted from the top of a 15 ft lighthouse at an angle of
depression of 20 degrees. how far from the base of the lighthouse is
the boat to nearest tenth?

Explanation:

Step1: Recall the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). For the angle of elevation problem (Question 20), \(\theta = 35^{\circ}\), the adjacent side \(x = 150\) ft (distance from the point on the ground to the building), and the opposite side \(y\) (height of the building) is what we want to find. So, \(\tan(35^{\circ})=\frac{y}{150}\).

Step2: Solve for \(y\)

We know that \(y = 150\times\tan(35^{\circ})\). Using a calculator, \(\tan(35^{\circ})\approx0.7\). Then \(y=150\times0.7 = 105\) ft.

For the angle of depression problem (Question 21):

Step1: Use the tangent function

The angle of depression is equal to the angle of elevation from the boat to the top of the lighthouse. The height of the lighthouse \(h = 15\) ft (opposite side) and let the distance from the base of the lighthouse to the boat be \(d\) (adjacent side). \(\tan(20^{\circ})=\frac{15}{d}\).

Step2: Solve for \(d\)

\(d=\frac{15}{\tan(20^{\circ})}\). Using a calculator, \(\tan(20^{\circ})\approx0.364\). Then \(d=\frac{15}{0.364}\approx41.2\) ft.

Answer:

Question 20: B. 105 feet
Question 21: C. 41.2 feet