Question

ABC below is a right triangle where the measure of AB is 6 units and the measure of ∠A is 50°. What would the area of the triangle be?

A. 18sin50°
B. 18tan50°
C. 6sin50°
D. 36sin50°

Answer 1

B. is the thing dear friend

Answer 2

18 tan 50

Option B

Explanation:

Given is a picture of triangle ABC.

The triangle is right angled at B.

AB =6 and angle A = 50

Using trig ratios we have

`(AB)/(AC) =(6)/(y) =cos50` where y is length of hypotenuse = AC

Solving y = 6sec 50

Area of triangle =
`(1)/(2) (AB)(AC) sin 50`

=
`(1)/(2) (6)(6sec50)(sin50)\\= 18 tan 50`