Answer:
a = [tex]\sqrt{7}[/tex]
Step-by-step explanation:
I think your question is missed of key information, allow me to add in and hope it will fit the original one.:
Suppose ABC is a right triangle with sides a, b, and c and right angle at C. Find the unknown side length using the Pythagorean theorem and then find the values of the six trigonometric functions for angle B. when b=3 and c=4.
My answer:
We will Pythagoras theorem, which states that the sum of squares of two legs of a right triangle is equal to the square of the hypotenuse of right triangle. Because the question says that ABC is a right triangle.
[tex]a^2+b^2=c^2[/tex]
Given that: b=3 and c=4
[tex]a^2+3^2=4^2a^2+9=16a^2+9-9=16-9a^2=7[/tex]
so a = [tex]\sqrt{7}[/tex]
We know that tangent relates opposite side of a right triangle with adjacent side.
[tex]\text{tan}(B)=\frac{a}{b}\\\text{tan}(B)=\frac{\sqrt{7}}{3}[/tex]
Please have a look at the attached photos.
