For the given triangle, CE = 8.0 units, CD = 4.0 units and m∠E = 27°.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 63°. It is given that the opposite side is CE and the adjacent side is CD. The hypotenuse of the triangle measures 9 units.
Assume the opposite side measures x units and the adjacent side measures y units.
To determine the length of the opposite side of the triangle, we use the sin of the given angle.
[tex]sin\theta = \frac{oppositeside}{hypotenuse}.[/tex]
To determine the length of the adjacent side of the triangle, we use the cos of the given angle.
[tex]cos\theta = \frac{adjacentside}{hypotenuse}.[/tex]
Step 2:
In the given triangle,
The length of the opposite side = x units,
The length of the adjacent side = y units,
The length of the hypotenuse = 9 cm,
The angle of the triangle = 63°.
[tex]sin\theta = \frac{oppositeside}{hypotenuse}, sin 63 = \frac{x}{9} , sin 63 = 0.891.[/tex]
[tex]x = 0.891(9) = 8.019.[/tex]
[tex]cos\theta = \frac{adjacentside}{hypotenuse}, cos 63 = \frac{y}{9} , sin 63 = 0.4539.[/tex]
[tex]y = 0.4539(9) = 4.0851.[/tex]
Since it is a triangle, the total angle is 180°.
So 63° + 90° + ∠E = 180°, ∠E = 180° - 153° = 27°.
Rounding the values off, we get CE = 8.0 units, CD = 4.0 units and m∠E = 27°.
P.S. You're not a dummy, no-one knows everything. We're all a work in progress.
