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decide which of the following statements are true based on the given triangle below. Assume the figure is drawn to scale that angle A is greater than angle B.

Decide Which Of The Following Statements Are True Based On The Given Triangle Below Assume The Figure Is Drawn To Scale That Angle A Is Greater Than Angle B class=

Sagot :

From the figure given, the triangle is a right triangle.

Since it is a right triangle, ∠C = 90 degrees

Assuming the figure is drawn to scale and ∠A is greater than ∠B, then we have the following:

m∠A = 90° - m∠B

Using the triangle angle sum theorem, ∠A + ∠B + ∠C = 180

since m∠C = 90°,

m∠B + m∠A = 90°

Thus, m∠A = 90 - m∠B,

Also,

[tex]\tan B=\frac{\sin B}{\cos B}[/tex]

Since ∠A is greater than ∠B, then ∠A = 60 and ∠B = 30

Thus,

[tex]\begin{gathered} \tan B=\frac{\sin B}{\cos B} \\ \\ \tan 30=\frac{\sin 30}{\cos 30} \end{gathered}[/tex]

ANSWER:

[tex]\begin{gathered} \tan B=\frac{\sin B}{\cos B} \\ \\ \\ m\angle A=90-m\angle B \end{gathered}[/tex]