| Direction: Q. 31 to 35 |
| An electrician wanted to repair a street lamp at a height of 15 feet. He places his ladder such that its foot is 8 feet from the foot of the lamp post as shown in the figure below: |
 |
| Based on the above information give the, answer of the following questions: |
A) \[\frac{8}{15}\]
B) \[\frac{8}{17}\]
C) \[\frac{15}{8}\]
D) \[\frac{15}{17}\]
Correct Answer: B
Solution :
| \[\cos R=\frac{\text{Side adjacent to angle R}}{\text{Hypotenuse}}=\frac{QR}{PR}\] |
| We will first calculate PR by using Pythagoras theorem in\[\Delta PQR\]. |
| So, \[P{{R}^{2}}=P{{Q}^{2}}+Q{{R}^{2}}={{(15)}^{2}}+{{8}^{2}}=289={{17}^{2}}\Rightarrow PR=17\]feet. |
| Therefore, \[\cos R=\frac{QR}{PR}=\frac{8}{17}\] |
| So, option [b] is correct. |
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