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kogti [31]
3 years ago
8

An angle measures 58.4° more than the measure of its complementary angle what is the measure of each angle?

Mathematics
1 answer:
avanturin [10]3 years ago
7 0

Answer:

15.8

74.2

Step-by-step explanation:

Call the two angles A and B

A = B + 58.4              Substitute for A

A + B =90

B + 58.4 + B = 90      Combine like terms  

2B + 58.4 = 90          Subtract 58.4

2B = 90 - 58.4

2B = 31.6                    Divide by 2

B = 15.8

A = 15.8 + 58.4           Fin A

A = 74.2

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In RST, RS = 7, RT = 10, and ST = 8. Which angle of RST has the smallest measure? A T BCANNT BE DETERMINDED C R D S
Scrat [10]

Answer:

Correct answer is option A. T

Step-by-step explanation:

Given that

In a \triangle RST, RS = 7, RT = 10, and ST = 8.

To find:

Smallest angle = ?

Solution:

We can use cosine rule here to find the angle.

Formula for cosine rule:

cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}

Where  

a is the side opposite to \angle A

b is the side opposite to \angle B

c is the side opposite to \angle C

Using the cosine rule:

cos T = \dfrac{ST^{2}+RT^{2}-RS^{2}}{2\times ST \times RT}\\\Rightarrow cos T = \dfrac{8^{2}+10^{2}-7^{2}}{2\times 8 \times 10}\\\Rightarrow cos T = \dfrac{64+100-49}{160}\\\Rightarrow cos T = \dfrac{115}{160}\\\Rightarrow \angle T = cos^{-1}(0.71875)\\\Rightarrow \angle T = 44.05^\circ

Now, let us use Sine rule to find other angles:

\dfrac{a}{sinA} = \dfrac{b}{sinB} = \dfrac{c}{sinC}

\dfrac{RS}{sinT} = \dfrac{ST}{sinR} = \dfrac{RT}{sinS}\\\Rightarrow \dfrac{7}{sin44.05} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow \dfrac{7}{0.695} = \dfrac{8}{sinR} = \dfrac{10}{sinS}\\\Rightarrow sin R = \dfrac{8 \times 0.695}{7}\\\Rightarrow R = 52.58^\circ

\Rightarrow sin S = \dfrac{10 \times 0.695}{7}\\\Rightarrow S = 83.14^\circ

Smallest angle is \angle T

Correct answer is option A. T

4 0
4 years ago
Which point is on the line y = -2x + 3?<br> (-2, -1)<br> (3, 3)<br> (3, -3)<br> (-3, -9)
Gnoma [55]
(-2, -1) so y = <span>-2(-2)  + 3 = 7; FALSE
</span>(3, 3) so y = -2(3)  + 3 = -3; FALSE<span>
(3, -3) </span>so y = -2(3)  + 3 = -3; TRUE<span>
(-3, -9) </span>so y = -2(-3)  + 3 = 9; FALSE 

answer
<span>(3, -3)</span>
8 0
4 years ago
Is 9.36 less. than. 9.359
konstantin123 [22]

Answer:

Its more because 9.36 has a bigger beginning then 9.359.





Ur welcome plzzz mark this as brainlest and thank me


4 0
4 years ago
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What is the square root of 25⁄4
Nadusha1986 [10]

Answer:

Exact Form:

5/2

Decimal Form:

2.5

Mixed Number Form:

21/2

7 0
4 years ago
Owen runs a pet store that sells rabbits. He wants to ensure he has more than 1 pound of dry food for every four rabbits he has
Lana71 [14]

Answer:

B) Owen can have a maximum of 22 rabbits in the store.

Step-by-step explanation:

Consider:

"He wants to ensure he has more than 1 pound of dry food for every four rabbits he has in the store."

It means, at least 0.25 pounds per rabbit. (1 pound divided by four)

"He currently has 5.7 pounds of dry food."

Inequality (r is the number of rabbits):

5.7\leq  0.25r\\22.8\leq r

According to the inequality, he can only have a maximum of 22 rabbits.

7 0
4 years ago
Read 2 more answers
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