Answer:
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
The height of the blimp above the ground is h = 153.884 yard
No, the fans will not be able to read the advertisement.
The exact angle if the blimp is at 150 feet is 45.74°
Step-by-step explanation:
From the summary of the information given :
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.
That statement above being illustrated in the attached diagram below for better understanding.
a. Which trigonometric ratio would you use to calculate how high the blimp will be above the 50 yard line?
The trigonometric ratio that can be used to calculate how high the blimp will be above the 50 yard line is :
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
b. How high above the ground is the blimp?
Using the above derived trigonometric ratio,
tan θ = [tex]\dfrac{opposite}{adjacent}[/tex]
[tex]tan \ 72^0 = \dfrac{h}{50}[/tex]
[tex]h =tan \ 72^0 \times {50}[/tex]
[tex]h =3.07768 \times {50}[/tex]
h = 153.884 yard
The height of the blimp above the ground is h = 153.884 yard
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?
No, the fans will not be able to read the advertisement.
This is because, 153.884 yard to feet
= 153.884 × 3
= 461.652 feet which is more than the maximum given 150 feet.
If not, what possible angle of elevation could we use?
The possible angle of elevation can be determined by taking the tangent of the trigonometric ratio.
SO
tan θ = [tex]\dfrac{h}{150}[/tex]
tan θ = [tex]\dfrac{153.884}{150 \ feet}[/tex]
tan θ = 1.026
θ = tan ⁻¹ (1.026)
θ = 45.74°
d. What is the exact angle if the blimp is at 150 feet?
The exact angle if the blimp is at 150 feet is 45.74°
