Question

1. determine the length of side s to the nearest tenth of a millimetre.
2. a ladder leans against a wall. the base of the ladder is on level ground 1.4 m from the wall. the angle between the ladder and the ground is 70°. how far up the wall does the ladder reach, to the nearest tenth of a metre?

a. 1.5 m
b. 3.8 m
c. 4.1 m
d. 0.5 m

Explanation:

Step1: Identify the right - triangle relationship

We have a right - triangle where the distance from the wall to the base of the ladder is the adjacent side ($a = 1.4$ m) to the angle between the ladder and the ground ($\theta=70^{\circ}$), and the height up the wall that the ladder reaches is the opposite side ($h$). We use the tangent function $\tan\theta=\frac{h}{a}$.

Step2: Rearrange the formula to solve for $h$

$h = a\times\tan\theta$.

Step3: Substitute the values

Substitute $a = 1.4$ m and $\theta = 70^{\circ}$ into the formula. Since $\tan70^{\circ}\approx2.7475$, then $h=1.4\times2.7475 = 3.8465$ m.

Step4: Round to the nearest tenth

Rounding $3.8465$ m to the nearest tenth gives $h\approx3.8$ m.

Answer:

b. 3.8 m