The diagram shows a pyramid $$$A B C D E$$$. The pyramid has a square horizontal base $$$A B C D$$$ with side $$$5 \mathrm{~cm}$$$. The vertex $$$E$$$ is vertically above the centre $$$O$$$ of the base. The height $$$O E$$$ of the pyramid is $$$9 \mathrm{~cm}$$$. Calculate the angle that $$$E C$$$ makes with the base $$$A B C D$$$. .............................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：0580_w21_qp_21 Year：2021 Question No：21

Answer:

$68.6$ or $68.55$ to $68.56$

Knowledge points:

E6.2.1 Apply Pythagoras’ theorem and the sine, cosine and tangent ratios for acute angles to the calculation of a side or of an angle of a right- angled triangle. (Angles will be quoted in degrees. Answers should be written in degrees and decimals to one decimal place.)

E6.2.2 Solve trigonometric problems in two dimensions involving angles of elevation and depression.

E6.2.3 Know that the perpendicular distance from a point to a line is the shortest distance to the line.

E6.5 Solve simple trigonometrical problems in three dimensions including angle between a line and a plane.

Answer:

Knowledge points:

Solution:

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