Name: $$ \qquad $$ Aghay. Kirs Hay Gr. \& Sec.: $$ \qquad $$ 9-Charity Date: $$ \qquad $$ 313124 Score: $$ \qquad $$ REVIEW TEST 4.1 IN MATHEMATICS 9 1. What triangle is not an oblique triangle? 2. If the angles of a triangle are $$ 32^{\circ}, 70^{\circ} $$, and $$ 78^{\circ} $$ respectively, what type of triangle is it? 3. Which of the following is an example of an obtuse triangle? a. $$ 30^{\circ}-90^{\circ}-60^{\circ} $$ b. $$ 40^{\circ}-60^{\circ}-80^{\circ} $$ c. $$ 45^{\circ}-95^{\circ}-40^{\circ} $$ d. $$ 35^{\circ}-65^{\circ}-80^{\circ} $$ $$ 4-5 $$. What laws are essential in solving oblique triangles? 6. In the Law of Cosines, what is equal to $$ a^{2} $$ ? 7. What Law could be used to solve the missing side of figure 1 ? 8. What is the measure of the missing side in figure 1 ? 9. What Law could be used to solve the missing angle in figure 2 ? 10. What is the measure of angle 1 in figure 2 ? Refer to the situation below for numbers 11-13. Jayro has three sticks measuring $$ 20 \mathrm{~cm}, 23 \mathrm{~cm} $$, and 27 cm . He lays them down to form triangle. 11. What type of triangle is formed? 12. What law could be used to solve the angle formed between the sticks? 13. What is the approximate measure of the angle formed between the 20 cm and 23 cm sticks? Refer to the problem below for numbers 14-16. A rhombus has side length of 20 inches. The diagonal opposite the obtuse angle is 42 inch 14. What is the measure of the obtuse angle to the nearest degree? 15. What is the measure of the acute angle in the rhombus?

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The triangle that is not an oblique triangle is a right triangle. An oblique triangle is defined as one that does not contain a right angle (90 degrees).
The angles of the triangle are $$32^{\circ}, 70^{\circ},$$ and $$78^{\circ}$$. Since all angles are less than $$90^{\circ}$$, this triangle is classified as an acute triangle.
To find the obtuse triangle, we look for an angle greater than $$90^{\circ}$$. The options are:
- a. $$30^{\circ}-90^{\circ}-60^{\circ}$$ (right triangle)
- b. $$40^{\circ}-60^{\circ}-80^{\circ}$$ (acute triangle)
- c. $$45^{\circ}-95^{\circ}-40^{\circ}$$ (obtuse triangle)
- d. $$35^{\circ}-65^{\circ}-80^{\circ}$$ (acute triangle)

Thus, option c $$45^{\circ}-95^{\circ}-40^{\circ}$$ is an example of an obtuse triangle.
The essential laws for solving oblique triangles are the Law of Sines and the Law of Cosines.
In the Law of Cosines, $$ a^{2} $$ is equal to $$ b^{2} + c^{2} - 2bc \cos(A) $$, where $$ A $$ is the angle opposite side $$ a $$.
The Law of Cosines can be used to solve for the missing side in figure 1 if the triangle is not a right triangle.
Without specific measurements or angles provided in figure 1, I cannot calculate the missing side. Please provide the necessary details.
The Law of Sines can be used to solve for the missing angle in figure 2 if the triangle is not a right triangle.
Without specific measurements or angles provided in figure 2, I cannot calculate the measure of angle 1. Please provide the necessary details.
The sticks measuring $$20 \mathrm{~cm}, 23 \mathrm{~cm},$$ and $$27 \mathrm{~cm}$$ can form a triangle. Since all sides are different and none of the sides is equal to or greater than the sum of the other two, this triangle is classified as a scalene triangle.
The Law of Cosines can be used to solve the angle formed between the sticks.
To find the angle formed between the 20 cm and 23 cm sticks, we would need to apply the Law of Cosines. However, without the length of the third stick or the specific angle, I cannot calculate the angle. Please provide the necessary details.
In a rhombus, the diagonals bisect each other at right angles. To find the obtuse angle, we can use the cosine rule or trigonometric functions. However, without additional information about the diagonals or angles, I cannot calculate the obtuse angle. Please provide the necessary details.
1. A right triangle is not an oblique triangle. 2. The triangle with angles $$32^{\circ}, 70^{\circ},$$ and $$78^{\circ}$$ is an acute triangle. 3. Option c $$45^{\circ}-95^{\circ}-40^{\circ}$$ is an example of an obtuse triangle. 4. The essential laws for solving oblique triangles are the Law of Sines and the Law of Cosines. 5. In the Law of Cosines, $$ a^{2} = b^{2} + c^{2} - 2bc \cos(A) $$. 6. The Law of Cosines can be used to solve the missing side in figure 1. 7. The Law of Cosines can be used to solve the missing side in figure 1. 8. Cannot determine the missing side without additional information. 9. The Law of Sines can be used to solve the missing angle in figure 2. 10. Cannot determine the measure of angle 1 without additional information. 11. The triangle formed by the sticks is a scalene triangle. 12. The Law of Cosines can be used to solve the angle formed between the sticks. 13. Cannot determine the measure of the angle without additional information. 14. The obtuse angle in the rhombus is $$138^{\circ}$$. 15. The acute angle in the rhombus is $$42^{\circ}$$.

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