Solve the right triangle, ΔABC, for the missing side and angles to the nearest tenth given sides a = 13.2 and b = 17.7.

Side c = 22.1

Angle A = 36.7°

Angle B = 53.2°

Angle C = 90.1°

Step-by-step explanation:

Triangle ABC is a right angle

Where given sides

a = 13.2

b = 17.7

We can find c using Pythagoras Theorem

Pythagoras Theorem for a right angle triangle=

c² = a² + b²

c = √(a² + b²)

c = √(13.2² + 17.7²)

c = 22.08008

≈To the nearest tenth = 22.1

We can solve for Angles A, B, C using Cosine rule

Angle A

a² = b² + c² - 2bc × Cos A

Cos A = b² + c² - a²/2bc

A = Arc cos ( b² + c² - a²/2bc)

A = Arc cos ( 17.7² + 22.1² - 13.2²/2 × 17.7 × 22.1)

A = 36.67563°

≈ To the nearest tenth = 36.7°

Angle B

b² = a² + c² - 2ac × Cos B

Cos B = a² + c² - b²/2ac

B = Arc cos (a² + c² - b²/2ac)

B = Arc cos(13.2² + 22.1² - 17.7²/ 2 × 13.2 ×22.1)

B = 53.21647°

≈Approximately to the nearest tenth = 53.2°

Angle C

c² = a² + b² - 2ab × Cos C

Cos C = a² + b² - c²/2ab

C = Arc cos ( a² + b² - c²/2ab)

C = Arc cos ( 13.2² + 17.7² - 22.1²/2 × 13.2 × 17.7)

C = 90.1079°

≈ to the nearest tenth = 90.1°

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.