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Mice21 [21]
3 years ago
14

Use the markings in the image to answer the following questions (drawing not to scale):

Mathematics
1 answer:
Marina86 [1]3 years ago
7 0
a. We can calculate all the sides using the given information.

b. 
- Length of a:
The first thing we are going to do is find the value of theta; to do it we are going to use arcosine: 
cos \alpha = \frac{5}{13}
\alpha =arcos( \frac{5}{13} )
\alpha =67.38

Next, since we know the the length of adjacent side of theta is 12, we can use the trig function cosine to find the length of a:
cos( \alpha )= \frac{adjacent.side}{hypotenuse}
cos(67.38)= \frac{12}{a}
a= \frac{12}{cos(67.38)}
a=31.20

- Length of b:
Since we already find the length of a, we just need to use the Pythagorean theorem to find the length of b:
b^2=a^2-12^2
b^2=31.20^2-12^2
b= \sqrt{31.20^2-12^2}
b=28.8

- Length of c
We already know the measure of angle theta, so we are going to use the trig function tangent to find the length of b:
tan( \alpha )= \frac{opposite.side}{adjacent.side}
tan(67.38)= \frac{12}{c}
c= \frac{12}{tan(67.38)}
c=5

- Length of d:
Since we already find the length of c, we are going to use the Pythagorean theorem to find the length of d:
d^2=c^2+12^2
d^2=5^2+12^2
d= \sqrt{5^2+12^2}
d=13

c. We can conclude that we have all the information we need to find the measures of all the sides of our triangles.
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