Option d: Angle A is 30 degrees, BC is 5 units
Option e: AC is 8 units, BC is 6 units
Explanation:
The triangle ABC has a right angle at C.
The length of the hypotenuse is 10 units.
The image of the triangle with this measurement is attached below:
Option a: Angle A is 20 degrees, BC is 2 units
[tex]\begin{aligned}\sin 20 &=\frac{2}{h y p} \\h y p &=\frac{2}{\sin 20} \\&=5.8476\end{aligned}[/tex]
Since, hypotenuse is 10 units, Option a is not correct answer.
Option b: AC is 7 units, BC is 3 units
[tex]\begin{aligned}A B &=\sqrt{7^{2}+3^{2}} \\&=\sqrt{49+9} \\&=\sqrt{58}\end{aligned}[/tex]
Since, hypotenuse is 10 units, Option b is not correct answer.
Option c: Angle B is 50 degrees, BC is 4 units
[tex]\begin{aligned}\cos 50 &=\frac{4}{h y p} \\h y p &=\frac{4}{\cos 50} \\&=6.222\end{aligned}[/tex]
Since, hypotenuse is 10 units, Option c is not correct answer.
Option d: Angle A is 30 degrees, BC is 5 units
[tex]\begin{aligned}\sin 30 &=\frac{5}{h y p} \\h y p &=\frac{5}{\sin 30} \\&=10\end{aligned}[/tex]
Since, hypotenuse is 10 units, Option d is the correct answer.
Option e: AC is 8 units, BC is 6 units
[tex]\begin{aligned}A B &=\sqrt{8^{2}+6^{2}} \\&=\sqrt{64+36} \\&=\sqrt{100} \\&=10\end{aligned}[/tex]
Since, hypotenuse is 10 units, Option e is the correct answer.
Thus, Option d and e are the correct answers.
In triangle ABC, Angle A is 30 degrees, BC is 5 units.
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Triangle ABC has a right angle at C and a hypotenuse AB.
If angle A is 30°:
sin(30) = BC/10
BC = 5 units
In triangle ABC, Angle A is 30 degrees, BC is 5 units.
Find out more on Trigonometric ratio at: https://brainly.com/question/24349828
