Solve each triangle. Round your answers to the nearest tenth

Mathematics

1 answer:

ivolga24 [154]2 years ago

7 0

You have to use the Law of Cosines here, since there's no other way to solve this. it's not a right triangle, so you can't use the Pythagorean Theorem. The Law of Cosines will help us find the missing side length then we will have to use the Law of Sines to find another angle. Then after that we will use the Triangle Angle-Sum theorem to finish it off. Ready? The Law of Cosines to find side b is $b^{2} = a^{2}+ c^{2} -2ac cosB$ and fill in the info we know, which is everything but the b. $b^{2} =(21) ^{2} +(29) ^{2} -2(21)(29)cos109$ . Doing all that math gives us that side b = 40.9 or 41. Now the Law of Sines to find missing angle A or C. Let's find A. $\frac{sinA}{21} = \frac{sin109}{41}$ . That gives us that angle A is 29. Now use the fact that all triangles add up to 180 to get that angle C is 42. And you're done!

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A radio station plays a total of 272 pop, rock, and hip-hop songs during a day. The number of pop songs is 3 times the number of

Norma-Jean [14]

Let the daily played number of pop songs be P, the number of rock songs be R and the number of hip-hop songs be H.

i)
"A radio station plays a total of 272 pop, rock, and hip-hop songs during a day"

means that : P+R+H=272

ii)
"The number of pop songs is 3 times the number of rock songs. "

so, P=3R

iii)
"The number of hip-hop songs is 32 more than the number of rock songs."

means: H=32+R

iv)

since both P and H can be written in terms of R, we have:

P+R+H=272

(3R)+R+(32+R)=272

3R+R+32+R=272

5R+32=272

5R=272-32=240

R=240/5=48

vi)

thus: P=3R=3*48=144, H=32+R= 32+48=80

Answer:

48 Rock, 144 Pop and 80 Hip-hop

5 0

2 years ago

86° 34° Х X = ____ degrees help quick pls

Rufina [12.5K]

Answer:

60 degrees

Step-by-step explanation:

The angles all have to add up to 180, so you can do

$34 + 86 +x = 180\\120 + x = 180\\x = 60$