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elixir [45]
3 years ago
6

Solve the right triangle, ΔABC, for the missing sides and angle to the nearest tenth given angle B = 39° and side c = 13.

Mathematics
1 answer:
hram777 [196]3 years ago
5 0

Answer:

Part 1) b=8.2\ units

Part 2) a=10.1\ units

Part 3) A=51\° and C=90\°

Step-by-step explanation:

see the attached figure with letters to better understand the problem

step 1

Find the side b

we know that

In the right triangle ABC

The function sine of angle B is equal to divide the opposite side angle B (AC) by the hypotenuse (AB)

sin(B)=AC/AB

we have

AB=c=13\ units

AC=b

B=39\°

substitute

sin(39\°)=b/13

solve for b

b=(13)sin(39\°)

b=8.2\ units

step 2

Find the side a

we know that

In the right triangle ABC

The function cosine of angle B is equal to divide the adjacent side angle B (BC) by the hypotenuse (AB)

cos(B)=BC/AB

we have

AB=c=13\ units

BC=a

B=39\°

substitute

cos(39\°)=a/13

solve for a

a=(13)cos(39\°)

a=10.1\ units

step 3

Find the measure of angle A

we know that

In the right triangle ABC

C=90\° ----> is a right angle

B=39\°

∠A+∠B=90° ------> by complementary angles

substitute the given value

A+39\°=90\°

A=90\°-39\°

A=51\°

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Answer:
294.14cm^2

Explanation:

First find the area of the whole piece of paper:
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Then find the area of the two semicircles, semicircle + semicircle = 1 circle:

Area of a circle= (radius squared)(pi):
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Subtract the area of the two semicircles from the whole paper area:
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I hope this isn’t too confusing :)


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3 years ago
At what rate percent will the interest on Rs. 6300 in 10 years be equal to its principal?​
grin007 [14]

Answer:

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3 years ago
Suppose the population of a certain city is 5289 thousand. It is expected to decrease to 4530 thousand in 50 years. Find the per
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Answer:

14.4% decrease

Step-by-step explanation:

Here is the formula for finding the percentage of decrease:

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3 years ago
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Answer:  i) 1 - 9x² - 12x

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<u>Step-by-step explanation:</u>

g(x) = 3x + 2       h(x) = 5 - x²

i) h(g(x))

  h(3x + 2) = 5 - (3x + 2)²

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iii) h(h(x))

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                 = -20 + 10x² - x⁴

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