Answered

Explore Westonci.ca, the premier Q&A site that helps you find precise answers to your questions, no matter the topic. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

In triangle ABC, angle bisectors line AD, line BE, and line CF meet at I. If DI = 3, BD = 4, and BI = 5, then compute the area of triangle ABC

Sagot :

MrRoyal

The area of triangle ABC is the amount of space on the triangle

The area of the triangle is 54.84 square units

How to determine the area of triangle ABC

Start by drawing the triangle (see attachment)

Next, calculate the measure of angle B using the following tangent ratio

[tex]\tan(B/2) = \frac 34[/tex]

This gives

[tex]\tan(B/2) = 0.75[/tex]

Take the arc tan of both sides

[tex]B/2 = 36.87[/tex]

Multiply by 2

[tex]B = 73.74[/tex]

Next, calculate the length of side AD using the following equation

[tex]AD = \tan(B) * BD[/tex]

This gives

[tex]AD = \tan(73.74) * 4[/tex]

[tex]AD =13.71[/tex]

The area of the triangle is then calculated as:

[tex]Area = AD * BD[/tex]

This gives

[tex]Area = 13.71 * 4[/tex]

[tex]Area = 54.84[/tex]

Hence, the area of the triangle is 54.84 square units

Read more about areas at:

https://brainly.com/question/24487155

View image MrRoyal
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.