Question

You focus your camera on a circular fountain. Your camera is at the vertex of the angel formed by tangents to the fountain. You estimate that the angle is 44°. What is the measure of the arc of the circular basin of the fountain that will be in the photograph?

Answer 1

Answer:

The measure of the arc of the circular basin = 136°

Step-by-step explanation:

The measure of an angle formed when two line intercepts outside a circle is half the difference of the measure of the intercepted arcs.

Mathematically, the is represented as:

Measure of an angle = 1/2(big angle - Small angle)

This values are given in the question

Measure of an angle = Measure of angle formed by tangents to the fountain = 44°

big angle is represented by = 360°-x

small angle is represented by = x

Therefore, we have

44° = 1/2( 360° - x -x)

44° = 1/2(360° - 2x)

Cross multiply

44° × 2 = 360° - 2x

88° = 360° - 2x

88° - 360° = - 2x

-272° = -2x

x = -272/-2

x = 136°

The measure of the arc of the circular basin = 136°