Question

You work for an advertising company and have been hired to place a blimp above a football stadium. The angle of elevation from a point directly under the goal post is 72° and the blimp will be directly above the 50 yard line. a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line? b. How high above the ground is the blimp? c. In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet. Will the fans be able to read the advertisement? If not, what possible angle of elevation could we use? d. What is the exact angle if the blimp is at 150 feet?

Answer 1

Answer:

a) tangent ; b) 153.88 yds ; c) No , less than or equal to 45° ; D) 45°

Explanation:

Given the following ;

From the triangle sketch :

Base length = 50 yards

Angle of elevation = 72°

a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line?

Using trigonometry :

The height of the blimp will be calculated using :

Tangent :

Tan θ = opposite / Adjacent

B.) How high above the ground is the blimp?

Using :

Tan θ = opposite / Adjacent

Θ = 72° ; adjacent = 52, opposite = height(h)

Tan 72° = h / 50

h = 3.0776835 * 50

h = 153.88 yds

C.) In order to be able to read the advertisement on the side of the blimp the highest the blimp can be is 150 feet. Will the fans be able to read the advertisement?

1 yard = 3 Feets

153.88 yards = 3 * 153.88

= 461.65 feets

No, because the height of the blimp is 461.65 Feets which is greater than 150 Feets.

To make viewing possible, the angle of elevation should be:

50 yards is equivalent to (3 * 50) = 150 feets

Max imum Height of blimp = 150 Feets

From pythagoras ;

Tanθ = 150 Feets / 150 Feets

Tanθ = 1

θ = tan^-1(1)

θ = 45°

To make viewing advertisement possible, angle of elevation should not exceed 45°

d.)If height of blimp is 150 Feets, then the exact angle of elevation will be 45°