Question 1: The indicated angle is 30°
Question 2: The indicated angle is 44°
Question 3: The indicated angle is 39°
Question 4: The indicated angle is 18°
Question 5: The indicated angle is 37°
Question 6: The indicated angle is 17°
Step-by-step explanation:
As all the triangles are right-angled triangle, trigonometric ratios can be used to find the indicated angles.
Let x be the angle
<u>Question 1:</u>
The according to the angle
P = 22
B = 38
Tangent ratio uses both base and perpendicular so,
![tan\ x=\frac{P}{B}\\tan\ x= \frac{22}{38}\\tan\ x=0.5789\\x=tan^{-1} (0.5789}\\x = 30.06\\x=30](https://tex.z-dn.net/?f=tan%5C%20x%3D%5Cfrac%7BP%7D%7BB%7D%5C%5Ctan%5C%20x%3D%20%5Cfrac%7B22%7D%7B38%7D%5C%5Ctan%5C%20x%3D0.5789%5C%5Cx%3Dtan%5E%7B-1%7D%20%280.5789%7D%5C%5Cx%20%3D%2030.06%5C%5Cx%3D30)
The indicated angle is 30°
<u>Question 2:</u>
According to the angle,
P = 28
B = 29
Again we will use tangent
![tan\ x =\frac{P}{B}\\tan\ x=\frac{28}{29}\\tan\ x=0.9655\\x=tan^{-1}(0.9655)\\x=43.99\\x=44](https://tex.z-dn.net/?f=tan%5C%20x%20%3D%5Cfrac%7BP%7D%7BB%7D%5C%5Ctan%5C%20x%3D%5Cfrac%7B28%7D%7B29%7D%5C%5Ctan%5C%20x%3D0.9655%5C%5Cx%3Dtan%5E%7B-1%7D%280.9655%29%5C%5Cx%3D43.99%5C%5Cx%3D44)
The indicated angle is 44°
<u>Question 3:</u>
According to angle,
P = 22
H = 35
![sin\ x=\frac{P}{H}\\sin\ x =\frac{22}{35}\\sin\ x=0.6286\\x=sin^{-1}(0.6286}\\x=38.94\\Rounding\ off\ to\ nearest\ degree\\x=39](https://tex.z-dn.net/?f=sin%5C%20x%3D%5Cfrac%7BP%7D%7BH%7D%5C%5Csin%5C%20x%20%3D%5Cfrac%7B22%7D%7B35%7D%5C%5Csin%5C%20x%3D0.6286%5C%5Cx%3Dsin%5E%7B-1%7D%280.6286%7D%5C%5Cx%3D38.94%5C%5CRounding%5C%20off%5C%20to%5C%20nearest%5C%20degree%5C%5Cx%3D39)
The indicated angle is 39°
<u>Question 4:</u>
According to angle,
B = 3
H = 9
We will use cos
![cos\ x =\frac{B}{H}\\cos\ x=\frac{3}{9}\\cos\ x=0.3333\\x=cos^{-1}(0.3333)\\x=18.43\\Rounding\ off\ to\ nearest\ degree\\x=18](https://tex.z-dn.net/?f=cos%5C%20x%20%3D%5Cfrac%7BB%7D%7BH%7D%5C%5Ccos%5C%20x%3D%5Cfrac%7B3%7D%7B9%7D%5C%5Ccos%5C%20x%3D0.3333%5C%5Cx%3Dcos%5E%7B-1%7D%280.3333%29%5C%5Cx%3D18.43%5C%5CRounding%5C%20off%5C%20to%5C%20nearest%5C%20degree%5C%5Cx%3D18)
The indicated angle is 18°
<u>Question 5:</u>
According to indicated angle,
B =35
H =46
![cos\ x =\frac{B}{H}\\cos\ x=\frac{35}{46}\\cos\ x=0.7609\\x=cos^{-1}(0.7609)\\x=37.2\\Rounding\ off\ to\ nearest\ degree\\x=37](https://tex.z-dn.net/?f=cos%5C%20x%20%3D%5Cfrac%7BB%7D%7BH%7D%5C%5Ccos%5C%20x%3D%5Cfrac%7B35%7D%7B46%7D%5C%5Ccos%5C%20x%3D0.7609%5C%5Cx%3Dcos%5E%7B-1%7D%280.7609%29%5C%5Cx%3D37.2%5C%5CRounding%5C%20off%5C%20to%5C%20nearest%5C%20degree%5C%5Cx%3D37)
The indicated angle is 37°
<u>Question 6:</u>
According to angle,
P = 15
H = 49
![sin\ x=\frac{P}{H}\\sin\ x =\frac{15}{49}\\sin\ x=0.3061\\x=sin^{-1}(0.3061}\\x=17.02\\Rounding\ off\ to\ nearest\ degree\\x=17](https://tex.z-dn.net/?f=sin%5C%20x%3D%5Cfrac%7BP%7D%7BH%7D%5C%5Csin%5C%20x%20%3D%5Cfrac%7B15%7D%7B49%7D%5C%5Csin%5C%20x%3D0.3061%5C%5Cx%3Dsin%5E%7B-1%7D%280.3061%7D%5C%5Cx%3D17.02%5C%5CRounding%5C%20off%5C%20to%5C%20nearest%5C%20degree%5C%5Cx%3D17)
The indicated angle is 17°
Keywords: Trigonometric Ratios, Right angled triangle
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