Question

In △ABC, the angles A and C are equal to 30◦ and 120◦ respectively, and the side AC = 20ft, find the length of the perpendicular from B upon AC produced.

Answer 1

We can start by drawing a diagram of the triangle ABC:

A

/ \

/ \

/ \

/ \

/ \

B ----------- C

We know that angle A is 30 degrees and angle C is 120 degrees, so angle B must be:

angle B = 180 - angle A - angle C

= 180 - 30 - 120

= 30 degrees

Now we can use the sine function to find the length of the perpendicular from B to AC produced. Let's call this length x:

sin(angle B) = perpendicular / hypotenuse

sin(30) = x / 20

We can solve for x by multiplying both sides by 20 and taking the sine of 30:

x = 20 sin(30)

x = 20 (1/2)

x = 10

Therefore, the length of the perpendicular from B upon AC produced is 10 feet.

Explanation: