Short Answer 
To solve for the unknown angle in a right-angled triangle, apply the SOH CAH TOA rules, where SOH stands for Sine, CAH for Cosine, and TOA for Tangent. With the given opposite and adjacent side lengths (4 and 3 blocks, respectively), use the TOA rule to calculate Tan∅ as 1.33, leading to an angle ∅ of approximately 53.13° using the inverse tangent function.
Step 1: Understand the SOH CAH TOA Rules
The SOH CAH TOA rules are essential for solving trigonometric problems related to right-angled triangles. These rules define how to relate the angles to the sides of the triangle:
- SOH: Sine = Opposite √∑ Hypotenuse
- CAH: Cosine = Adjacent √∑ Hypotenuse
- TOA: Tangent = Opposite √∑ Adjacent
Step 2: Identify Your Variables
In this particular problem, you need to identify the lengths of the sides related to the angle you’re solving for. Here are the values given:
- Opposite: 4 blocks
- Adjacent: 3 blocks
- Angle (‚àÖ): Unknown
Step 3: Calculate the Unknown Angle Using TOA
Using the TOA rule, you can now find the angle ‚àÖ. You will plug in the values for the opposite and adjacent sides and solve:
- Calculate Tan‚àÖ: Tan‚àÖ = Opposite √∑ Adjacent = 4 √∑ 3 = 1.33
- Find the angle ∅: Use the inverse tangent function, ∅ = Tan⁻¹(1.33)
- The calculated angle is ∅ = 53.13°.