Question

URGENT!!!! A ladder is leaning up against a house at a 49∘ angle. Jim, who is 5 feet tall, is standing upright on the ladder forming angle B. He is also holding a board which rests 2 feet below him on the ladder. According to the triangle in the figure and the given information, find the shortest length of the board needed. (Round your final answer to the nearest tenth place.)

Answer 1

6.5 feet

Explanation:

Based on the Cosines Law, we have:

`cos(B) = (c^(2) + a^(2) - b^(2) )/(2 * a * c)`

If we isolate b (which is our x in this problem), we have

`b = \sqrt{a^(2)  + c^(2)  - 2 * a * c * cos(B)}`

We have

a: 2

c: 5

B: 131 (since it's the complement of the 49 degrees angle: 180 - 49).

So, we plug these numbers in the formula....

`b = \sqrt{2^(2)  + 5^(2)  - 2 * 2 * 5 * cos(131)}  = 6.49`

We round it up to the tenth of the unit... to get 6.5