(a) The diagonals of a rhombus are 10.2 cm and 9.3 cm long. Calculate, correct to one decimal place, the perimeter of the rhombus.
(b) Given that (sin x = frac{3}{5}, 0° < x < 90°), find the value of (5cos x – 4tan x).
Explanation
(a)
Let a side of the rhombus be n.
Then (n^{2} = 4.65^{2} + 5.1^{2})
= (21.6225 + 26.01 )
(n^{2} = 47.6325)
(n = sqrt{47.6325} = 6.902 cm)
Hence, the perimeter of the rhombus = 4n
= (4 times 6.902)
= (27.608 cm approxeq 27.6 cm) (to 1 d.p)
(b) Right- angled triangle ABC
(sin x = frac{3}{5}), Thus, (m^{2} = 5^{2} – 3^{2} = 25 – 9 = 16)
(m = 4).
(cos x = frac{4}{5} implies 5cos x = 5 times frac{4}{5} = 4)
(tan x = frac{3}{4} implies 4tan x = 4 times frac{3}{4} = 3)
(5cos x – 4tan x = 4 – 3 = 1).