Question

given the information in this picture which trigonomic identity can be used to solve for the height of the blue ladder that is leaning against the building​

Answer 1

• Perpendicular=50ft=P
• Hypotenuse=h=?

`\\ \tt\hookrightarrow sin\theta=(P)/(H)`

`\\ \tt\hookrightarrow sin47=(50)/(h)`

`\\ \tt\hookrightarrow h=(50)/(sin47)`

`\\ \tt\hookrightarrow h=(50)/(0.73)`

`\\ \tt\hookrightarrow h=68.4ft`

Answer 2

sine

sin = o/h

Explanation:

The ladder leaning against the building has created a right triangle.

A right triangle is made up of 2 legs (at 90° to each other) and a hypotenuse (longest side).

Trig ratios help us calculate side lengths and interior angles of right triangles:

• sin(x) = O/H
• cos(x) = A/H
• tan(x) = O/A

where x is the angle, O = the side opposite to the angle, A = the side adjacent to the angle, H = hypotenuse

From inspection of the diagram, we need to find the hypotenuse (H) and we have been given the angle (x) and the side opposite to the angle (O):

Therefore, we can use the trig ratio sin(x) = O/H to determine H:

⇒ sin(47) =50/H

⇒ H = 50/sin(47)

⇒ H = 68.36637305... = 68 ft (nearest foot)