Sagot :
Answer:
1. a= 12.3cm
[For the triangle where a ,b, c are the length of the sides and α, β, γ are the opposite angles, the law of sines: [tex]\frac{a}{sin(\alpha )} = \frac{b}{sin(\beta )} = \frac{c}{sin(γ)}\\[/tex]or γ
Hence, a = c
sin(∠C) sin(∠A)
Given:
*∠ACB= 90 [angle C is a right angle]
*a or CB= 11
*∠A= 63
Find: c
[substitute the given values, therefore..
[tex]\frac{a}{sin(90)} = \frac{11}{sin(63)}[/tex]
[use the trigonometric trivial identity where sin(90) = 1
[tex]\frac{a}{1} = \frac{11}{sin (63)}[/tex] [apply rule [tex]\frac{a}{1} = a[/tex] ]
[tex]a=\frac{11}{sin(63)}\\[/tex]
[ Try it on your scientific calculator and you will get
a = 12.34558 or 12.3
2. Evaluate
Answer= 11/4
A.
[tex]3(cos30)^2 + 2(sin30)^2[/tex]
[Get the value of cos(30) from trigonometric values table]
[tex]3 (\frac{\sqrt{3} }{2} )^2 + 2(sin30)^2[/tex]
[To raise [tex]\frac{\sqrt{3} }{2}[/tex] to a power, raise both numerator and denominator to the power and then divide.
[tex]3 (\frac{\sqrt{3^2} }{2^2} ) + 2(sin30)^2[/tex]
[Then, make [tex]3 (\frac{\sqrt{3^2} }{2^2} )[/tex] as a single fraction]
[tex]\frac{3(\sqrt{3})^2}{2^2} + 2(sin30)^2[/tex]
B.
[Get the value of sin(30) from the trigonometric values table]
[tex]\frac{3(\sqrt{3})^2}{2^2} + 2(\frac{1}{2})^2[/tex]
[Calculate [tex]\frac{1}{2}[/tex] to the power of 2 to get [tex]\frac{1}{4}[/tex] , then multiply it to 2 to get [tex]\frac{1}{2}[/tex] ]
[tex]\frac{3(\sqrt{3})^2 }{2^2} + \frac{1}{2}[/tex]
[To add or subtract expressions, expand them to make their denominators the same. Least common multiple of [tex]2^{2}[/tex] and 2 is 4. Multiply [tex](\frac{1}{2}) (\frac{2}{2} )[/tex]
[tex]\frac{3(\sqrt{3})^2}{4} + \frac{2}{4}[/tex]
[Since they have the same denominator, add their numerators then copy the denominator to make them a single fraction]
[tex]\frac{3(\sqrt{3})^2+ 2}{4}[/tex] [ the square of [tex]\sqrt{3}[/tex] is 3]
[tex]\frac{(3)(3)}{2^2} + \frac{1}{2}[/tex] [Multiply 3 and 3 to get 9, then calculate 2^2 to get 4]
[tex]\frac{9}{4} + \frac{1}{2}[/tex] [ add 9/4 and 1/2 to get 11/4. It is important to learn how to solve fractions with unlike/different denominators]