# The sail on a toy boat is in the shape of an isosceles triangle. Its legs are 12 inches long and its base angles measure 70°. How long to the nearest hundredth of an inch, is the base of the sail?

Jan 30, 2016

base$= 8.20$ $\text{inches}$

#### Explanation:

If we were to cut the whole isosceles triangle in half, two right triangles would be produced:

Using a primary trigonometric ratio , we can determine the base length of one of the right triangles. In this case, we can use cosine. Recall that:

$\cos \theta = \text{adjacent"/"hypotenuse}$

To find the base length, or the "adjacent," substitute your known values into the formula:

$\cos \theta = \text{adjacent"/"hypotenuse}$

$\cos {70}^{\circ} = \frac{\text{adjacent}}{12}$

$12 \left(\cos {70}^{\circ}\right) = \text{adjacent}$

$\text{adjacent} \approx 4.10$ $\text{inches}$ $\Rightarrow$ rounded off to two decimal places

Recall that the base length of the left triangle is equal to the base length of the right triangle. Thus, multiply $4.10$ $\text{inches}$ by $2$ to get the base length of the whole isosceles triangle:

$4.10 \cdot 2$
$\approx 8.20$ $\text{inches}$

$\therefore$, the base length of the sail is approximately $8.20$ $\text{inches}$.