Question

Can someone help me please?

Answer 1

see explanation

Explanation:

(a)

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the given angles from 180° for B

∠ B = 180° - (90 + 63)° = 180° - 153° = 27°

(b)

Using the sine ratio in the right triangle

sin63° =
`(opposite)/(hypotenuse)` =
`(BC)/(AB)` =
`(15)/(x)` ( multiply both sides by x )

x × sin63° = 15 ( divide both sides by sin63° )

x =
`(15)/(sin63)` ≈ 16.8 ( to 1 dec. place )

(c)

Using the tangent ratio in the right triangle

tan63° =
`(opposite)/(adjacent)` =
`(BC)/(AC)` =
`(15)/(y)` ( multiply both sides by y )

y × tan63° = 15 ( divide both sides by tan63° )

y =
`(15)/(tan63)` ≈ 7.6 ( to 1 dec. place )