Question

Suppose a triangle has vertices A, B and C and has the following measurements:m∠C=93∘¯¯¯¯¯¯¯¯AC=39.8 cm¯¯¯¯¯¯¯¯BC=32.6 cmStart by drawing a diagram of this triangle and labeling the known values.What is the length of AB in cm?¯¯¯¯¯¯¯¯AB= cm   What is the degree measure of ∠A?m∠A= °   What is the degree measure of ∠B?m∠B=  °

Answer 1

EXPLANATION

If a triangle has vertices A,B and C with the given measures:

The draw is as follows:

The length of AB is given by the Pythagorean Theorem as shown as follows:

`\text{Hypotenuse}^2=32.6^2+39.8^2^{}`

Computing the powers:

`\text{Hypotenuse}^2=1062.76+1584.04`

Adding both numbers:

`Hypoten\\u se^2=2646.8`

Applying the square root to both sides:

`\text{Hypotenuse}=\sqrt[]{2646.8}`

Simplifying:

The degree measure of
`(\sin A)/(A)=(\sin B)/(B)`Substituting terms:

`(\sin 93)/(AB)=(\sin A)/(39.8)`

Multiplying both sides by 39.8 and substituting terms:

`39.8\cdot(\sin 93)/(51.44)=\sin A`

Multiplying numbers:

`0.77\cdot\sin 93=\sin A`

Simpifying:

`0.77\cdot0.99=0.77=\sin A`

Applying sin-1 to both sides:

`\sin ^(-1)(0.77)=A`

Switching sides:

`A=50.25\degree`

Then, by applying the Sum of Interior Angles of a Triangle Theorem, we know that the sum of interior angles is equal to 180 degrees,thus:

`180-50.25-93=B=36.75\degree`

Hence,

1) AB= 51.44 cm

2) A= 50.25°

3) B= 36.75°