Question

In a Δ ABC, ABC = 90° and angle ACB = 30°, then find AB : AC.​

Answer 1

GIVEN : (IN ∆ABC)

=> Angle ABC = 90°

=> Angle ACB = 30°

TO FIND :

=> AB : AC = ?

STEP - BY - STEP EXPLANATION :

NOTE –––––»

NOTE –––––» (REFERS TO THE ATTACHMENT)

Answer 2

Answer:  the ratio of AB : AC = 1 : 2

Step-by-step explanation:

Given that

In  Δ ABC, angle ABC = 90° and angle ACB = 30°,

To find AB : AC.​

• Draw a triangle ABC with angle ABC = 90° and angle ACB = 30°. Label the angles and sides of the triangle, with AB as the opposite side of angle ACB, and AC as the hypotenuse.

• Since angle ABC = 90°, we know that triangle ABC is a right triangle.

• we know that sum of all the angles of a triangle is 180°

So, by using angle sum property

∠ABC+ ∠ACB + ∠BAC =180°

90° + 30° +∠BAC = 180°

∠BAC = 60°

By applying the sine rule

Sin A/BC = Sin B/AC  = Sin C/AB

Sin 90/AC = Sin 30 / AB

AB/ AC =Sin 30 / Sin 90

AB/AC = 1/2

AB : AC = 1 : 2

OR We can also solve by another way as follows

1. Draw a triangle ABC with angle ABC = 90° and angle ACB = 30°. Label the angles and sides of the triangle, with AB as the opposite side of angle ACB, and AC as the hypotenuse.

2. Since angle ABC = 90°, we know that triangle ABC is a right triangle.

3. Use the property of a right triangle, that the angle opposite to the right angle is always 90°.

4. Now, use the properties of a 30-60-90 triangle to find the ratio of AB to AC.

5. In a 30-60-90 triangle, the ratio of the two sides that are not the hypotenuse are 1:2.

6. In this case, AB is the side opposite of angle ACB, which is 30°. Therefore, AB is the side with the ratio of 1 in the 1:2 ratio.

AC is the hypotenuse of the triangle and is the side with the ratio of 2 in the 1:2 ratio.

Therefore, the ratio of AB to AC in the triangle is 1:2

This can also be proved by using the property of 30-60-90 triangles that the hypotenuse is always twice the length of the shorter leg. Since AB is the shorter leg, AB=AC/2

With this information, we can say that the ratio of AB to AC is 1:2

• The sine rule is a trigonometry rule that relates the lengths of the sides of a triangle to the sine of its angles. It states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all three sides of the triangle. The sine rule is often used to find the length of a side of a triangle when the lengths of the other two sides and the size of the angles opposite those sides are known. It is also known as "the law of sines". This rule can be used in any triangle, not only right triangles. The sine rule can be written as a/sin A = b/sin B = c/sin C = 2R (R being the circumradius)

To learn more about "the law of sines" from the link below

https://brainly.com/question/30248261

To learn more about trigonometry rule from the link below

https://brainly.in/question/54170140

#SPJ3