The answers are 24.44°, 35.10°, PS is 21.20, ∠CDB is 68.73°, and length of the ramp is 44.65
It is given the right angle triangle in the picture.
It is required to find the sides and angles.
What is the trigonometric ratio?
The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.
In the first diagram:
[tex]\rm tan x = \frac{opposite}{adjacent }[/tex]
[tex]\rm tanx =\frac{10}{22}[/tex]
[tex]\rm x = tan^-^1(\frac{10}{22} )\\\\\rm x = 24.44[/tex]
In the second diagram:
[tex]\rm cos x = \frac{adjacent}{hypotenuse} \\\\\rm cosx = \frac{27}{33} \\\\\rm x = cos^-^1(\frac{27}{33})\\\\\rm x = 35.10[/tex]
In the third diagram:
∠QRS = 28° and QR = 39
[tex]\rm tan28 = \frac{opposite}{39} \\\\\rm opposite = 39 \times tan28[/tex]
opposite QS = 20.74
[tex]\rm sin76 = \frac{QS}{pS} \\\\\rm PS = \frac{20.74}{sin76} \\\\PS = 21.34[/tex]
In the fourth diagram:
[tex]\rm tan47 = \frac{opposite }{18} \\\\\rm Opposite = 19.30[/tex]
[tex]\rm cosx = \frac{7}{19.30} \\\\\rm x = cos^-^1(\frac{7}{19.30} )\\\\\ \rm x = 68.73[/tex]Where x = ∠CDB
In the last:
We can use sin ratio to find the length of the ramp:
[tex]\rm sin 21 =\frac{16}{x}\\ \\\rm x =\frac{16}{sin21} \\\\\rm x = 44.65[/tex] Where x is the length of the ramp
Thus, the answers are 24.44°, 35.10°, PS is 21.20, ∠CDB is 68.73°, and length of the ramp is 44.65.
Know more about trigonometry here:
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