Question

B ВaAbСLet c=12, and a=4.020. What is tan(A) in radians? Round to 3 decimal places.

Answer 1

Tan (A) = 0.109 radians

Step-by-step explanation:

The figure given is a right angles triangle

Given that AB = c is the hypotenus

AC = b = adjacent

BC = a = opposite

Tan A can be calculated using SOH CAH TOA

Tan A = opposite / adjacent

Tan A = BC / AC

BC = a = 4.020

We need to find b uisng pythagoras theorem

`\begin{gathered} c^2=a^2+b^2 \\ 12^2=4.020^2+b^2 \\ 144=16.1604+b^2 \\ \text{Collect the like terms} \\ b^2\text{ = 144 - 16.1604} \\ b^2\text{ = 127.8396} \\ b\text{ = }\sqrt[]{127.8396} \\ b\text{ = 11.307} \end{gathered}`

b = 11.307

Tan A = 4.020 / 11.307

Tan A = 0.3555

A = tan ^-1 (0.3555)

A = 19.570 degrees

Convert degrees to radian

since 1 pi = 180 degrees

x pi = 19.570

Cross multiply

19.570 * 1 = x * 180

x = 19.570 / 180

x = 0.109

Therefore, tan (A) is 0.109 radians