Question

What is the measure of angel A rounded to nearest whole number ?

A. 30 degrees
B. 28 degrees
C. 2 degrees
D. 62 degrees

Answer 1

Use inverse cosine here because you have the side adjacent to angle A and the hypotenuse. On your calculator, press the 2nd key then cosine to see this on your display
`cos^(-1)` then enter 8/17 to give you an angle measure of 62 degrees.

Answer 2

D. 62 degrees

Explanation:

Here, ABC is a right angles triangle,

In which,

AB = 8 units,

AC = 17 units,

∠B = 90°,

By the pythogorous theorem,

`AC^2=AB^2+BC^2`

`17^2=8^2+BC^2`

`289=64-BC^2`

`225=BC^2`

`\implies BC=15\text{ unit}`

By the law of sine,

`(sin A)/(BC)=(sin B)/(AC)`

`(sin A)/(15)=(sin 90^(\circ))/(17)`

`sin A = (15)/(17)`

`\implies A= 61.9275^(\circ)\approx 62^(\circ)`

Hence, the measure of angle A is 62 degrees,

Option D is correct.