Question

1. a ladder leans against a vertical wall and makes an angle of 76° with the ground. the foot of the ladder is 1.8 m from the base of the wall. how high up the wall is the top of the ladder, to the nearest tenth of a metre?

Explanation:

Step1: Identify the trigonometric relationship

We have a right - triangle where the distance from the base of the wall to the foot of the ladder is the adjacent side ($x = 1.8$ m) to the given angle $\theta=76^{\circ}$, and the height up the wall where the top of the ladder touches is the opposite side ($y$). We use the tangent function since $\tan\theta=\frac{y}{x}$.
$\tan\theta=\frac{y}{x}$

Step2: Substitute the known values

Substitute $\theta = 76^{\circ}$ and $x = 1.8$ m into the formula. We know that $\tan76^{\circ}\approx4.01078$.
$y=x\tan\theta$
$y = 1.8\times\tan76^{\circ}$
$y=1.8\times4.01078$

Step3: Calculate the value of $y$

$y=7.219404$ m
Rounding to the nearest tenth of a metre, $y\approx7.2$ m.

Answer:

$7.2$ m