Using the diagram below, write the ratio of cos M. 2. What is the complement of cot 30°? 3. Given tan Q = 2/3, find the length of side QR in surd form.

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Asked on May 9, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-05-09T15:56:36.256Z

Welcome back — been a while! Let's pick up where you left off. 1. Using the diagram below, write the ratio of M. Step 1: Identify the sides relative to angle M. In the given right-angled triangle: • The side adjacent to angle M is 15. • The hypotenuse (the side opposite the right angle) is 17. Step 2: Write the ratio for M. The cosine of an angle in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. M = AdjacentHypotenuse Substitute the values from the diagram: M = (15)/(17) The ratio of M is (15)/(17). 2. What is the complement of 30^? Step 1: Understand the term "complement of a trigonometric ratio". The complement of a trigonometric ratio of an angle is its co-function of the complementary angle. For example, the complement of is (90^ - ). Step 2: Find the complementary angle of 30^. The complementary angle of 30^ is 90^ - 30^ = 60^. Step 3: Identify the co-function of cotangent and apply it to the complementary angle. The co-function of cotangent is tangent. Therefore, the complement of 30^ is (90^ - 30^) = 60^. The complement of 30^ is 60^. 3. Given Q = (2)/(3), find the length of side QR in surd form. Step 1: Identify the sides relative to angle Q from the diagram. In the given right-angled triangle: • The side opposite angle Q is labeled 2. • The side adjacent to angle Q is QR. Step 2: Use the given Q ratio to set up an equation. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Q = OppositeAdjacent Substitute the values from the diagram and the given ratio: (2)/(QR) = (2)/(3) Step 3: Solve for QR. Since the numerators are equal, the denominators must also be equal. QR = 3 Step 4: Express the length of QR in surd form. An integer can be expressed in surd form by taking its square root and squaring it. QR = sqrt(3^2) QR = sqrt(9) The length of side QR in surd form is sqrt(9). Send me the next one 📸

Accepted Answer · 2026-05-09T15:56:36.256Z

Welcome back — been a while! Let's pick up where you left off. 1. Using the diagram below, write the ratio of M. Step 1: Identify the sides relative to angle M. In the given right-angled triangle: • The side adjacent to angle M is 15. • The hypotenuse (the side opposite the right angle) is 17. Step 2: Write the ratio for M. The cosine of an angle in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. M = AdjacentHypotenuse Substitute the values from the diagram: M = (15)/(17) The ratio of M is (15)/(17). 2. What is the complement of 30^? Step 1: Understand the term "complement of a trigonometric ratio". The complement of a trigonometric ratio of an angle is its co-function of the complementary angle. For example, the complement of is (90^ - ). Step 2: Find the complementary angle of 30^. The complementary angle of 30^ is 90^ - 30^ = 60^. Step 3: Identify the co-function of cotangent and apply it to the complementary angle. The co-function of cotangent is tangent. Therefore, the complement of 30^ is (90^ - 30^) = 60^. The complement of 30^ is 60^. 3. Given Q = (2)/(3), find the length of side QR in surd form. Step 1: Identify the sides relative to angle Q from the diagram. In the given right-angled triangle: • The side opposite angle Q is labeled 2. • The side adjacent to angle Q is QR. Step 2: Use the given Q ratio to set up an equation. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side. Q = OppositeAdjacent Substitute the values from the diagram and the given ratio: (2)/(QR) = (2)/(3) Step 3: Solve for QR. Since the numerators are equal, the denominators must also be equal. QR = 3 Step 4: Express the length of QR in surd form. An integer can be expressed in surd form by taking its square root and squaring it. QR = sqrt(3^2) QR = sqrt(9) The length of side QR in surd form is sqrt(9). Send me the next one 📸

Using the diagram below, write the ratio of cos M. 2. What is the complement of cot 30°? 3. Given tan Q = 2/3, find the length of side QR in surd form.

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Using the diagram below, write the ratio of cos M. 2. What is the complement of cot 30°? 3. Given tan Q = 2/3, find the length of side QR in surd form.

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