Question

Find the points where the diagonals of Rhombus A(-2, -1), B(-1, 4), C(4, 5) and D(3, 0) bisect at right angles​

Answer 1

Answer:

A church is 600 m due west of a flagpole. A statue is on a bearing of 160° from the church and on a bearing of 220° from the flagpole.

To find : The distance of the church from the statue.

solution : see diagram, here we put church at point C , statue at point B and flagpole at A on a line X which is parallel to Y.

from diagram, it is clear that ∠ACB = ∠ABC = 20°

so distance between flagpole and statue is 600m.

now distance between church and statue i.e., CB

here using formula,

cos140° = {AB² + AC² - BC²}/2AB AC

⇒2AB AC cos140° = AB² + AC² - BC²

⇒BC = √{AB² + AC² - 2AB AC cos140°}

= √{600² + 600² - 2 × 600² × cos140°}

= 1128 m

Therefore the distance between church and statue is 1128 m