Question

From the adjoining figure, find the value of θ.

Answer 1

Given:

In the adjoining figure, the base whole horizontal length = 30 cm.

The right-most angle of the large triangle = 30°.

The left slant side from left end of base to the top vertex = 20 cm.

A perpendicular (altitude) is drawn from the top vertex to the base.

Step-wise calculation:

1. Let the altitude be h.

Consider the right triangle on the right base = 30 cm and angle at right end = 30°:

`tan 30^circ = "Opposite"/"Adjacent"`

= `h/30`

Since, `tan (30^circ) = 1/sqrt(3)`:

`1/sqrt(3) = h/30`

`h = 30/sqrt(3)`

`h = 10sqrt(3)` cm

2. Now consider the left right-angled triangle formed by the altitude h, the left base segment, and the slant side 20 cm. This slant side is the hypotenuse.

At the leftmost point, the angle is θ. 

So, `sin θ = "Opposite"/"Hypotenuse"`

= `h/20`

 `sin θ = (10sqrt(3))/20`

= `sqrt(3)/2`

θ = 60°