The recommended angle for a firefighting ladder is 75 degrees. When a 110-foot ladder is put up against a building at this angle, the base of the ladder is about 28 feet from the building. The base of the ladder is 8 feet above the ground. How high on the building will the ladder reach?

114.37 ft

Step-by-step explanation:

If we model this situation as a right triangle, where the hypotenuse is the length of the ladder (), the opposite leg is the height the ladder will reach , and the adjacent leg is the distance between the base of the ladder and the building (); we have two options:

1) Using trigonometric functions, since we are given the angle

2) Using the Pithagorean Theorem

Any of the options will give a similiar result. So, let's choose the Pithagorean Theorem:

Isolating :

Adding to this height the extra height of (since the base of the ladder is at this distance above the ground, perhaps held by a firefighter truck):

This is the height the ladder will reach

answer: 25 is the correct answer

step-by-step explanation:

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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