Question

use the sliders to solve the triangle given a = 40 and b = 20.
use the interactive figure to find your answer. use the left and right arrow keys to move along a slider as needed.
click here to launch the interactive figure.
state whether the given statement is true or false. if side b doubles in length to 40, angle b also doubles. choose the correct answer below
true
false

Explanation:

Step1: Calculate the original angle B

Assume it is a right - triangle. Using the tangent function \( \tan B=\frac{b}{a} \). Given \( a = 40 \), \( b = 20 \), then \( \tan B=\frac{20}{40}=\frac{1}{2} \). So \( B=\arctan(\frac{1}{2})\approx26.57^{\circ} \)

Step2: Calculate the new angle B when \( b = 40 \)

Now \( \tan B=\frac{40}{40}=1 \). So \( B=\arctan(1) = 45^{\circ} \)
Since \( 45^{\circ}
eq2\times26.57^{\circ}\approx53.14^{\circ} \)

Answer:

False