The Law of Sines and the Law of Cosines – Basics

Q1

On a circular stage with diameter

, three cameras are installed at points

,

, and

as shown in the diagram. Points

and

are at the opposite ends of a diameter. When looking from point

toward points

and

, the angle formed

. Answer the following questions about trriagle

.

(1)

Find

.

Subjective Answer

(2)

Using trigonometric ratios, find the lengths of segments

and

.

Subjective Answer

(3)

Fill in the boxes with the appropriate numbers.

Subjective Answer

Q2

There is a triangle

with

,

, and

. Find the value of

.

Q3

For the triangle

with

,

and

, find the value of

.

Q4

For the triangle

with

and

, find the radius of the circle that circumscribes to

.