Question

The distance from Wei to Mahdi is 12 feet and the distance from Wei to Lakshmi is 6 feet. A triangle is drawn connecting the positions of Wei, Lakshmi, and Mahdi. How far is Mahdi from Lakshmi if the angle marking Wei’s position is 88°?

13.6 ft

13.2 ft

13.3 ft

14.2 ft

Answer 1

I think the answer is 13.2

Answer 2

Refer to the attached image.

Assume that Wei is standing at position 'A', Mahdi is standing at position 'B' and Lakshmi is standing at the position 'C'.

Since, the distance from Wei to Mahdi(AB) is 12 feet, and the distance from Wei to Lakshmi(AC) is 6 feet.

The angle marking Wei’s position($\angle A$) is 88°

By law of cosines, which states:

"In triangle ABC, with angles A, B and C. Side opposite to angle A is 'a', side opposite to angle B is 'b' and side opposite to angle C is 'c'. This formula is used to find the third side of a triangle when we know two sides and the angle between them. Therefore, it states:

$a^{2}=b^{2}+c^{2}-2bc\cos A$

In triangle ABC, c=12 feet , b=6 feet and angle A = 88 degrees.

$a^{2}=(6)^{2}+(12)^{2}-(2 \times 12 \times 6 \times \cos 88^{\circ})$

$a^{2}=174.97$

$a=\sqrt{174.97}$

a=13.2 feet

a=13.2 feet

The distance from Mahdi to Lakshmi is 13.2 feet.

Therefore, Option B is the correct answer.