Question

Find the missing sides a & b. Type sqrt for the square root symbol.b4a60°a =b=

Answer 1

Right triangles

When one of the angles of a triangle measures 90°, we call it a right triangle

In any right triangle, the trigonometric ratios can be applied to compute unknown sides of the triangle

In the given triangle, we have one side and one angle in a right triangle

The angle of 60° is defined by two sides. The side at his left side is the hypotenuse and the side at his right is the adjacent side, which value we know (4).

The trigonometric ratio called cosine is defined by:

`\text{cos 60\degree= }\frac{adjacent\text{ side}}{hipotenuse}=(4)/(a)`

From that equation, we can calculate the value of the side a. Multiply both sides by a:

`a\cdot\text{cos 60\degree= }4`

Solving:

`a=\frac{4}{\text{cos 60\degree}}=(4)/((1)/(2))=8`

Now we find the value of b by applying the sine of the angle, defined by:

`\sin \text{ 60\degree= }\frac{opposite\text{ side}}{hipotenuse}=(b)/(a)=(b)/(8)`

Multiplying the equation by 8:

`b=8\cdot\sin \text{ 60\degree=8}\cdot(√(3))/(2)=4√(3)`

Giving the answer in the required format:

a = 8

b = 4 sqrt 3