Question

NUMBER 1. Solve the word problem and draw the triangle.

Answer 1

The ladder is 16ft long and it is leaning against a wall so that it makes a 50º angle with the ground.

First, draw a sketch of the described scenario so that you can visualize it:

The ladder leaning against the wall represents the hypothenuse of a right triangle, the ground distance of the ladder, and the wall represents the legs of the triangle.

Given that you know the measure of one of the acute angles of the triangle and the length of the hypothenuse, you can determine the height of the wall by applying trigonometric ratios.

The wall is on the opposite side to the angle, the trigonometric ratio that includes the opposite side and the hypothenuse is the sine, defined as follows:

`\sin \theta=(opposite)/(hypothenuse)`

Replace the expression with the length of the ladder (hypothenuse) and the measure of the angle:

`\sin 50=(x)/(16)`

To determine the value of x multiply both sides by 16

`\begin{gathered} 16\sin 50=16\cdot(x)/(16) \\ 16\sin 50=x \\ x=12.256\cong12ft \end{gathered}`

The ladder will reach up to 12ft on the wall.