Question

Jermaine, Henrietta, and Michael are each at home. Their relative locations are shown in the diagram.



What is the distance between Michael's house and Henrietta's house?



Enter your answer in the box. Round your final answer to the nearest mile.

mi
A simple map layout in shape of a scalene triangle. The vertex at left top is labeled as Henrietta house, vertex at right top is labeled as Jermaine house, and vertex at bottom is labeled as Michael house. The interior angle made at Jermaine house is labeled as 26 degrees. The distance between Jermaine house and Michael house is labeled as 19 miles. The distance between Jermaine house and Henrietta house is labeled as 27 miles.

Answer 1

SOLUTION

GIVEN

Jermaine, Henrietta, and Michael are each at home. Their relative locations are shown in the diagram.

TO DETERMINE

What is the distance between Michael's house and Henrietta's house?

Enter your answer in the box. Round your final answer to the nearest mile.

FORMULA TO BE IMPLEMENTED

$\sf{ {a}^{2} = {b}^{2} + {c}^{2} - 2bc \cos A}$

EVALUATION

Here it is given that the distance between Jermaine house and Michael house is labeled as 19 miles.

The distance between Jermaine house and Henrietta house is labeled as 27 miles.

The interior angle made at Jermaine house is labeled as 26°

Thus b = 27 , c = 19 , A = 26°

Let a = The distance between Michael's house and Henrietta's house

$\sf{ {a}^{2} = {(27)}^{2} + {(19)}^{2} - 2 \times 27 \times 19 \times \cos {26}^{ \circ} }$

$\sf{ \implies \: {a}^{2} = 729 + 361 - 2 \times 513 \times 0.89879 }$

$\sf{ \implies \: {a}^{2} = 167.84 }$

$\sf{ \implies \: {a} = 12.9549 \approx \: 13 }$

FINAL ANSWER

The distance between Michael's house and Henrietta's house = 13 miles

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. locate the following points on the cartesian plane(aEr) (0,a),(a,0),(-a, 0),(0,-a)...

https://brainly.in/question/26822338

2. Distance of a point A(-2,0) from x-axis is _______ units.

https://brainly.in/question/28760447