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Trigonometric Ratios and Identities · Paper 2 — Free Maths AA SL Practice Questions

1MasterySAQ-SDefinitions of sine, cosine, and tangents6 marksPaper 2~9 min

A ladder of length

5\,\text{m}

is placed against a vertical wall. The foot of the ladder rests on horizontal ground. The ladder makes angle

\theta

with the ground, where

0^\circ < \theta < 90^\circ

. The height of the top of the ladder above the ground is

h\,\text{m}

, and the horizontal distance from the foot of the ladder to the wall is

x\,\text{m}

(a)

Show that

h = 5\sin\theta

and

x = 5\cos\theta

. [2 marks]

(b)

Given that

x = 1.5

, calculate the value of

\theta

, giving your answer in degrees correct to 3 significant figures. [2 marks]

(c)

Find the value of

\theta

, where

0^\circ < \theta < 90^\circ

, for which

h + x

is a maximum. [2 marks]

Solutions

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