Chapter 18

Subtract \(15^{\circ} 47^{\prime}\) from \(28^{\circ} 13^{\prime}\)

Convert (a) \(24^{\circ} 42^{\prime}\) (b) \(78^{\circ} 15^{\prime} 26^{\prime \prime}\) to degrees and decimals of a degree.

Convert \(45.371^{\circ}\) into degrees, minutes and seconds.

State the general name given to the following angles: (a) \(159^{\circ}\) (b) \(63^{\circ}\) (c) \(90^{\circ}\) (d) \(227^{\circ}\)

Find the angles complementary to (a) \(41^{\circ}\) (b) \(58^{\circ} 39^{\prime}\)

Two straight lines \(A B\) and \(C D\) intersect at 0 . If \(\angle A O C\) is \(43^{\circ}\), find \(\angle A O D, \angle D O B\) and \(\angle B O C\).

\(A B C\) is an isosceles triangle in which the unequal angle \(B A C\) is \(56^{\circ} . A B\) is extended to \(D\) as shown in Fig. 18.13. Determine the angle \(D B C\).

A rectangular shed \(2 \mathrm{~m}\) wide and \(3 \mathrm{~m}\) high stands against a perpendicular building of height \(5.5 \mathrm{~m} . \mathrm{A}\) ladder is used to gain access to the roof of the building. Determine the minimum distance between the bottom of the ladder and the shed.

Construct a triangle whose sides are \(6 \mathrm{~cm}\), \(5 \mathrm{~cm}\) and \(3 \mathrm{~cm}\).

Construct a triangle \(A B C\) such that \(a=6 \mathrm{~cm}\), \(b=3 \mathrm{~cm}\) and \(\angle C=60^{\circ} .\)

Construct a triangle \(P Q R\) given that \(Q R=5 \mathrm{~cm}, \angle Q=70^{\circ}\) and \(\angle R=44^{\circ}\)

Construct a triangle \(X Y Z\) given that \(X Y=5 \mathrm{~cm}\), the hypotenuse \(Y Z=6.5 \mathrm{~cm}\) and \(\angle X=90^{\circ}\).