Two identical ladders

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

Two identical ladders, each of length

L

m, lean against the same vertical wall on smooth ground. Ladder A makes an angle of

40^{\circ}

with the ground, while Ladder B makes an angle of

65^{\circ}

with the ground. Without using tables or a calculator, answer the following. (i) Express the height

h_A

reached by the top of Ladder A on the wall in terms of

L

and a trigonometric ratio of

40^{\circ}

. No numerical value of the ratio is to be used. (ii) Similarly, express the height

h_B

reached by the top of Ladder B on the wall in terms of

L

and a trigonometric ratio of

65^{\circ}

. (iii) Compare

h_A

and

h_B

and state which ladder reaches higher up the wall. Support your answer with clear reasoning, without evaluating any trigonometric ratio.