5cm
4cm
3√3 cm
\(\frac{10\sqrt{3}}{3}\)cm
Correct answer is D
Let each of the unknown side be x.
\(10^{2} = x^{2} + x^{2} - 2(x)(x) \cos 120\)
\(100 = 2x^{2} - 2x^{2} \cos 120\)
\(100 = 2x^{2} + x^{2} = 3x^{2}\)
x = \(\sqrt{\frac{100}{3}}\)
= \(\frac{10}{\sqrt{3}}\) x \(\frac{\sqrt{3}}{\sqrt{3}}\)
x = \(\frac{10\sqrt{3}}{3}\)cm
If sin \(\theta\) = cos \(\theta\), find \(\theta\) between 0° and 360°
45o, 225o
135o, 315o
45o, 315o
135o, 225o
Correct answer is A
sin \(\theta\) = cos \(\theta\) 0 \(\leq\) \(\theta\) \(\leq\) 360°
The acute angle where sin \(\theta\) = cos \(\theta\) = 45°
But at the third Quadrant Cos \(\theta\) = -ve; sin \(\theta\) = -ve.
at the 3rd quadrant, value with respect to Q is
(180 + Q) where Q = acute angle
(180 + 45) = 225°
The two solution are 45°, 225°
The angle between latitudes 30oS and 13oN is
17o
33o
43o
53o
Correct answer is C
The angle between 2 latitudes one in northern hemisphere and the other in southern hemisphere and the other in southern hemisphere is the sum of their latitudes.
∴ Total angle difference = (30 + 13) = 43o
Find the area of the sector of a circle with radius 3m, if the angle of the sector is 60o
4.0m2
1m2
4.7m2
5.0m2
Correct answer is C
Area of sector
\(\frac{\theta}{360}\) x \(\pi\)r2, \(\theta\) = 60o, r = 3m
= \(\frac{60}{360}\) x \(\frac{12}{7}\) x 3 x 3
\(\frac{1}{6}\) x \(\frac{22}{7}\) x 9
= \(\frac{33}{7}\)
= 4.7m2
find the radius of a sphere whose surface area is 154cm2 (\(\pi = \frac{22}{7}\))
7.00cm
3.50cm
3.00cm
1.75cm
Correct answer is B
Surface area = 154cm2 (area of sphere)
4\(\pi\)r2 = 154
r\(\sqrt{\frac{154}{4\pi}}\)
= 3.50cm