HELPPPP 80 POINTS Solve the right triangle. Round your answers to the nearest tenth

Mathematics

1 answer:

aev [14]2 years ago

5 0

answer:

A=46°

a=17.983 (tenths- 18, hundredths- 17.98)

b=17.366 (tenths- 17.4, hundredths- 17.37)

explanation:

1. find angle A

it shows that the angle corresponding with the side length of 25 is a right angle, meaning it's 90°. using that information and the angle given to us (44°), we're able to find the missing angle. since all the angles in a triangle always add up to 180°, we can add the two angles together and then subtract that from 180° to find the missing angle.

90°+44°=134°

180°-134°=46°

A=46°

2. find side a

using the law of cosines, we're able to find the length of side a. cosine of an angle equals $\frac{adjacent}{hypotenuse}$ . we'll be using angle B (44°) for our angle. after we plug in the values, we can just solve the equation to find side a.

cosine44°= $\frac{a}{25}$
(multiply both sides by 25)

25cosine44°=a
a=17.983

3. find side b

finding the length of side b is very similar to how you found side a. you can use the law of cosines again (make sure you use the right side lengths and angles!), but i used the law of sines. the sine of an angle equals $\frac{opposite}{hypotenuse}$ . we're going to be using the same angle for this.