Question

Consider the triangle.

Triangle A B C. Side A B has a length of 5, and side A C has a length of 5. Angle B is 30 degrees, angle C is 90 degrees, and angle A is unknown.

Angle A =
Angle B = 30°

Angle C = 90°



AB = 10

AC = 5

BC =

Answer 1

Angle A = 60°

BC= 8.7 ........

Answer 2

∠A=60°,side BC=5√3 units

Step-by-step explanation:

Given:

ΔABC,side AB=10 units

side AC=5 units

∠ABC=30°

∠ACB=90°

To find:

∠BAC,side AC

Solution:

In ΔABC,∠B=30°,∠C=90°.....................................(given)

∴By angle addition property

∠A+∠B+∠C=180°

∴∠A+30°+90°=180°

∴∠A=60°-----------------------------(putting the like terms together)

Here,

∠A=60°

∠B=30°

∠C=90°

∴ΔABC is a 30°-60°-90° triangle.

BC is the side opposite to ∠A which is 60°

∴By 30°-60°-90° triangle theorem

side BC=√3AC

∴side BC=√3×5

∴side BC=5√3 units.

Hence,∠A=60 and side BC=5√3 units.