Trigonometry Structured Questions | Cambridge O Level Mathematics (Syllabus D)

Question 1 of 4 · 8 marks

Trigonometry · 1 - Pythagoras' Theorem

4 parts

Mathematics (Syllabus D) 4024 · Question 1Paper 2 · Calculator[8 marks]

A solar energy firm plans a composite land plot $ABCD$ . $AB = 15\,\mathrm{m}$ and $AD = 10\,\mathrm{m}$ . Point $E$ lies on $AB$ such that $DE \perp AB$ and $EB = 9\,\mathrm{m}$ .

(a)

Show that $AE = 6\,\mathrm{m}$ and calculate the exact perpendicular height $DE$ .

[2]

(b)

Calculate the length of the diagonal $DB$ .

[2]

(c)

Point $C$ is placed such that $CD \perp BC$ and $CD = 7\,\mathrm{m}$ . Calculate the exact length of side $\ce{BC}$ in simplified surd form $k\sqrt{6}$ .

[2]

(d)

Calculate the total area of the plot $ABCD$ .

[2]