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In right triangle ABC, ZC is a right angle, m ZA = 52, AC = 10.01, and AB = c.

sin 52° 0.788

cos 52° 0.616

tan 52° 1.280

What is the measurement of AB?

If necessary, round your answer to two decimal places, like this: 42.53

Respuesta :

Answer:

The measurement of AB is 16.25 units.

Step-by-step explanation:

In right triangle ABC, ∠C is a right angle, m∠A = 52° , AC = 10.01, and AB = c.

We need to find the measurement of AB.

∠C is a right angle, it means AB is hypotenuse.

In a right angle triangle,

[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]

[tex]\cos A=\dfrac{AC}{AB}[/tex]

[tex]\cos (52^\circ)=\dfrac{10.01}{c}[/tex]

[tex]0.616=\dfrac{10.01}{c}[/tex]

[tex]c=\dfrac{10.01}{0.616}[/tex]

[tex]c=16.25[/tex]

Hence, the measurement of AB is 16.25 units.