Question

12 ABC and ACD are right-angled triangles.

DC = 8cm
Angle ADC = 45°
Angle ABC = 20°
D
45°
A
8 cm C
Work out the length of AB.
Give your answer correct to 3 significant figures.
20°
B

Answer 1

Answer: AB = 23.390 cm

Explanation:

We can quickly find the length of AB using a few principles:

Triangle-Angle-Sum: all the angles of the triangle equal 180.

180 - (45 + 90) = 45

The measure of <DAC is 45 degrees.

45-45-90 Triangle Length Rule: the two sides opposite the 45 angles are congruent. This means that AC is 8 cm.

Now we just use the sine function:

sin(20) = AC/AB ; sin(20) = 8/AB ; AB = 8/sin(20) ; AB = 23.390 cm.