Question

At a crime scene police find a person in Myrtle Beach shot while sunbathing on the pier. The pier is 20 feet high. The shot came 20 degrees from the parallel. How far was the shooter standing down the beach when the gun was fired?
Select one:
a. 30 feet away
b. 45 feet away
c. 55 feet away
d. 70 feet away

A person was hiking on a trail in Greenville County Park they were shot in the leg. Before he was shot, he had climbed to a height 45 vertical feet from the bottom of the mountain. The shooter was at angle of 40 degrees parallel to the mountain. How far was the shooter when he shot the person?

Select one:
a. 32 feet
b. 87 feet
c. 54 feet
d. 18 feet

A police officer shot a man running from a crime scene on a bridge that was 100 feet high. The bullet struck the victim 25 degrees to the parallel. Approximately how far away was the police officer when she fired her weapon?

Select one:
a. 500 feet
b. 380 feet
c. 217 feet
d. 78 feet

Answer 1

QUESTION 1 

The diagram to visualise this question is shown in the first picture below

We model this as a right angle triangle and we can use trigonometry ratio to find $x$ which is the distance between the shooter and the pier.

$tan(x)= \frac{opposite}{adjacent}$
$tan(70)= \frac{x}{20}$
$x=20tan(70)$
$x=54.94...$ which rounded to 55 feet

QUESTION 2

Referring to the second diagram, we have
$tan(x)= \frac{opposite}{adjacent}$
$tan(50)= \frac{x}{45}$
$x=45tan(50)$
$x=53.6289....$ which round to 54 feet

QUESTION 3

The length of $x$ is given
$tan(x)= \frac{opposite}{adjacent}$
$tan(65)= \frac{x}{100}$
$x=100tan(65)$
$x=214.45...$ which round to 214

Answers:
Question 1 is C
Question 2 is C
Question 3 is [there is no option for 214 feet]