Question

Find the area of the right angled triangle with hypotenuse 5 cm and one of the acute angle is 48°30'.
(Refer the trigonometric table for the values)

• A. 6.2093525 ${cm}^2$
• B. 6.2052935 ${cm}^2$
• C. 6.3025925 ${cm}^2$
• D. 6.2035925 ${cm}^2$

Answer 1

The correct option is D 6.2035925 ${cm}^2$

From the figure,
$sin\theta =\frac{AB}{AC}$
sin48°30' $=\frac{AB}{5}$
0.7490 $=\frac{AB}{5}$ [$\because$ sin48°30' = 0.7490]
5 $\times$ 0.7490 = AB
AB = 3.7450 cm

From the figure,
$cos\theta =\frac{BC}{AC}$
cos48°30' $=\frac{BC}{5}$
0.6626 $=\frac{BC}{5}$ [$\because$ cos48°30' = 0.6626]
5 $\times$ 0.6626 = BC
BC = 3.313 cm

$Areaofrighttriangle=\frac{1}{2}\times bh$

$=\frac{1}{2}\times BC\times AB$

$=\frac{1}{2}\times 3.313\times 3.745$
= 1.6565$\times$3.7450
$=6.2035925{cm}^2$