Loading [MathJax]/jax/output/SVG/jax.js
 
+0  
 
0
3
1
avatar+936 

In triangle ABC, BC=32, tanB=35, and tanC=14. Find the area of the triangle.

 Jan 30, 2025
 #1
avatar+130383 
+1

side AB  is contained on the line

y = (3/5)x

 

side AC is  contained on the line

y = -(1/4)(x -32)  = (-1/4)x + 8

 

The x intersection of these lines is

 

(3/5)x  = -(1/4)x + 8

 

[ 3/5 + 1/4] x  = 8

 

[17/20]x =8

 

x = 8 *20 / 17  = 160 /17

 

And the y value at this  point =  (3/5)(160 /17)  = 96/17  = the altitude...call this AD

 

[ABC]  =  (1/2) BC * AD   =  (1/2)  32 * 96/17 =  1536  /  17  

 

 

cool cool cool

 Jan 30, 2025

2 Online Users

avatar