Question

A rectangle measures 15cm by20cm find the angle between its diagonal

Answer 1

Answer:

Let ABCD is a rectangle in which AB=CD=15cm ,BC=DA=20cm , and B is on origin , Coordinate of B (0,0) , A(0,15) ,C(20,0) and D(20,15).

Slope of diagonal BD(m1)=(15–0)/(20–0)=3/4

Slope of diagonalAC(m2)=(0–15)/(20–0)-3/4

let p be the angle between diagonals.

tan p=(m1-m2)/(1+m1.m2)

tan p=(3/4+3/4)/(1–9/16)

tan p=(6/4)/(7/16)

tan p=6/4×16/7=24/7

p= tan inverse (24/7) , Answer.