In right ∆LMN, sin M = 0.759. What is cos N? A. 0.121 B. 0.241 C. 0.349 D. 0.651 E. 0.759
1 answer:
Answer:
E. 0.759
Step-by-step explanation:
You can take this right triangle to have a base length side LM , height of LN and a hypotenuse of MN
The sine of angle ∠LMN is 0.759, find the value of ∠LMN
∠LMN=49.38°
Find angle ∠LNM
You know sum of angles in a triangle add up to 180°, given that this is a right-triangle, the base angle is 90° hence
∠LNM=180°-(90°+49.38°)
∠LNM= 180°-139.38°=40.62°
Find cos 40.62°
Cos 40.62°=0.7590
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<u><em>Answer:</em></u>
Area of the polygon = 59 in²
<u><em>Explanation:</em></u>
From the given diagram, we can note that the given polygon is composed of an upper triangle, a side triangle and a rectangle
<u>Therefore:</u>
Area of polygon =
area of upper triangle + area of side triangle + area of rectangle
<u>1- getting the area of the upper triangle:</u>
<u>We have:</u>
base of triangle = 7 in
height of triangle = 6 in
<u>Therefore:</u>
Area of upper triangle = in²
<u>2- getting the area of the side triangle:</u>
<u>We have:</u>
base of triangle = 4 in
height of triangle = 5 in
<u>Therefore:</u>
Area of upper triangle = in²
<u>3- getting the area of the rectangle:</u>
<u>We have:</u>
length of rectangle = 7 in
width of rectangle = 4 in
<u>Therefore:</u>
Area of rectangle = length x width = 7 x 4 = 28 in²
<u>4- getting the total area of the polygon:</u>
Area of polygon =
area of upper triangle + area of side triangle + area of rectangle
<u>Therefore:</u>
Area of polygon = 21 + 10 + 28 = 59 in²
Hope this helps :)