Answer:
Step-by-step explanation:
1. Use the Pythagorean theorem
[tex] a^2 + b^2 = c^2 [/tex]
In the Pythagorean Theorem equation, a^2 + b^2 = c^2, the two sides called a and b are the legs which are the sides that form the right angle. The side called c is the hypotenuse and is the side opposite the right angle.
In this problem, the legs are x and 6.2 m. Those are called a and b.
The hypotenuse is 12.7 m which is c.
[tex] a^2 + b^2 = c^2 [/tex]
[tex] x^2 + (6.2~m)^2 = (12.7~m)^2 [/tex]
[tex] x^2 + 38.44~m^2 = 161.29~m^2 [/tex]
[tex] x^2 = 122.85~m^2 [/tex]
[tex] x = \sqrt{122.85~m^2} [/tex]
[tex] x = 11.1~m [/tex]
2.
[tex] \tan A = \dfrac{opp}{adj} [/tex]
[tex] \tan 15^\circ = \dfrac{18}{x} [/tex]
[tex] x\tan 15^\circ = 18 [/tex]
[tex] x = \dfrac{18}{\tan 15^\circ} [/tex]
[tex] x = 67.2 [/tex]
3. The triangle has a 45-deg angle and a 90-deg angle.
45 + 90 + m<3 = 180
m<3 = 45
The third angle also measures 45 deg. This is a special case called 45-45-90 triangle. The sides opposite the congruent angles are congruent, so x = y. Now we can use the Pythagorean theorem.
[tex] a^2 + b^2 = c^2 [/tex]
[tex] x^2 + x^2 = (\sqrt{10})^2 [/tex]
[tex] 2x^2 = 10 [/tex]
[tex] x^2 = 5 [/tex]
[tex] x = \sqrt{5} [/tex]
[tex] x = 2.24 [/tex]
[tex] y = 2.24 [/tex]
