Question

In △abc, ∠b is a right angle, ab⎯⎯⎯⎯⎯=1091⎯⎯⎯⎯√ab¯=1091 meters, bc⎯⎯⎯⎯⎯=30bc¯=30 meters, and ca⎯⎯⎯⎯⎯=100ca¯=100 meters. what is tan(∠a)? 91√109110 310310 103103 91√3913 391√91

Answer 1

Answer: $\text{tan a}= \frac{3\sqrt{91} }{91}$

Step-by-step explanation:

Since, in the triangle abc,

ab = 10√91 unit, bc = 30 unit, ca = 100 unit and m∠b = 90°

⇒ $\text{tan a} = \frac{bc}{ab}$

⇒ $\text{tan a} = \frac{30}{10\sqrt{91}}$

⇒ $\text{tan a} =\frac{3}{\sqrt{91}}$

⇒ $\text{tan a} = \frac{3\times \sqrt{91}}{\sqrt{91}\times \sqrt{91}}$

⇒ $\text{tan a} = \frac{3\sqrt{91}}{91}$

Which is the required value of tan(∠a).