The diagram shows an open box $$$A B C D E F G H$$$ in the shape of a cuboid. $$$A B=20 \mathrm{~cm}, B C=18 \mathrm{~cm}$$$ and $$$A E=16 \mathrm{~cm}$$$. A thin $$$\operatorname{rod} A G X$$$ rests partly in the box as shown. The rod is $$$40 \mathrm{~cm}$$$ long. Calculate the angle the rod makes with the base of the box. .............................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：0580_m20_qp_42 Year：2020 Question No：8(b)(ii)

Answer:

$30.7$ or $30.73$ to $30.74 \ldots$

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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