Question

Joshua has a ladder that is 18 ft long. He wants to lean the ladder against a vertical wall so that the top of the ladder is 17.7 ft above the ground. For safety reasons, he wants the angle the ladder makes with the ground to be no greater than 78°. Will the ladder be safe at this height?

Answer 1

For safety reasons \theta should not be greater than 70 and with the current scenario\theta= 79.52

the ladder will not be safe at this height

\theta= 79.52

Arithmetic

Question Parameters:

Joshua has a ladder that is 18 ft long.

He wants to lean the ladder against a vertical wall so that the top of the ladder is 17.7 ft

Generally the equation for the angle ABC is mathematically given as

Let ∠ABC = \theta

In the right angle triangle ACB,

Hence

sin ∠ABC  = AC / AB

sin \theta = 17.7 / 18

$\theta = sin-1 (17.7 / 18)\\\\\theta = 79.52$

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