Question

Lucy has to run two errands. She starts from home and travels 3 miles south to the post office. From the post office, she travels 4 miles east to the gas station. Then, from the gas station, she travels 5 miles to return home. The entire trip forms a triangle. What was the smallest angle made in her trip?

Answer 1

Answer:

Smallest angle = $36.87^\circ$

Step-by-step explanation:

Given that:

Let the home be at the point A.

Lucy travels 3 miles south to reach point B.

Then 4 miles to east to reach point C and then

returns to home traveling 5 miles making it a triangle for the whole journey.

This travel is nothing but forms a right angled $\triangle ABC$, right angled at point B.

To find:

Smallest angle in the travel.

Solution:

In a triangle, the smallest angle is the angle opposite to the smallest side.

Therefore, the $\angle C$ will be the smallest.

We can use tangent trigonometric ratio here:

$tan\theta = \dfrac{Perpendicular}{Base}$

$tan C = \dfrac{AB}{BC}\\\Rightarrow tan C = \dfrac{3}{4}\\\Rightarrow \angle C=tan^{-1}{0.75}\\\Rightarrow \angle C=36.87^\circ$

Therefore, the answer is:

Smallest angle = $36.87^\circ$