Problem Solving

AAPL wrote: ↑

Thu Apr 02, 2020 6:06 am

Official Guide

A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

A. 35
B. 42
C. 35√3
D. 7+35√3
E. 7+42√3

OA D

Here's an idea of what's going on....

When we compare the big triangle with the BASE 30-60-90 special triangle (which you must memorize for test day!), we can see that the hypotenuse of the big triangle is 35 times as long as the hypotenuse of the base triangle.
This means the big triangle is 35 times the size of the base triangle.

This means that, on the big triangle, the side opposite the 60 degree angle must be 35√3


Now before we (incorrectly) choose answer choice C, we must keep in mind that the question tells us the base of the ladder is 7 feet above the ground...


So, the TOTAL distance from the top of the ladder to the ground = 35√3 + 7

Answer: D

Cheers,
Brent

AAPL wrote: ↑

Thu Apr 02, 2020 6:06 am

Official Guide

A ladder of a fire truck is elevated to an angle of 60° and extended to a length of 70 feet. If the base of the ladder is 7 feet above the ground, how many feet above the ground does the ladder reach?

A. 35
B. 42
C. 35√3
D. 7+35√3
E. 7+42√3

OA D

We are given that the ladder of a fire truck is elevated to an angle 60 degrees above the ground and that the ladder has a length of 70 feet. We are also given that the ladder is 7 feet above the ground. The best thing to do in this situation is to draw a diagram.



Notice that the resulting triangle in the sketch is a 30-60-90 right triangle. Based on the given info, we don’t know that the ladder is leaning against a building whose side is perpendicular to the ground. The ratio of the sides of a 30-60-90 right triangle is x : x√3 : 2x. We see that the hypotenuse length of 70 feet is equal to the "2x" from the 30-60-90 ratio. Thus, we can set up an equation and solve for x.

70 = 2x

x = 35

Because x = 35, we know that the side opposite the 60-degree angle or, in this case, the height of the ladder, is 35√3. The height of the ladder is 35√3 feet and the base of the ladder is 7 feet above the ground; thus, we know that the ladder reaches a total height above the ground of 35√3 + 7 feet.

Answer D