USE TRIGONOMETRY TO FIND THE UNKNOWN IN TRIANGLE CIRCUMSCRIBING CIRCLE

Problem 1 :

Use trigonometry to find x in each diagram (correct to1 dec. pl.).

i)

Solution:

Given, AB = 10 cm

MB = 5 cm

𝜃 = 50°

By using trigonometry formula,

x = 6.5 cm

Problem 2 :

Solution :

Given, ∠POQ = 140°

So, ∠POR = 70°

PQ = 12.6 cm

So, PR = 6.3 cm

By using trigonometry formula,

Problem 3 :

Solution:

Given, ∠MON = 126°

OM = 7.3 cm

MN = 6.5 + 6.5

MN = 13 cm

Problem 4 :

Find the radius of a circle in which a chord of length 14 cm subtends an angle of 70° at the centre. (Give the answer correct to one decimal place.)

Solution:

So, the radius of the circle is 6.6 cm.

Problem 5 :

A chord subtends an angle of 110° at the centre of a circle of radius 5.6 cm. Find the length of the chord correct to one decimal place.

Solution:

So, the length of the chord is 9.16 cm.