Chapter 10 - Geometry - 10.2 Triangles - Exercise Set 10.2 - Page 629: 46

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(a) The length of the base of a right triangle is 5 m and the length of the hypotenuse is 6 m. The height of the right triangle can be calculated by using the Pythagorean Theorem. Compute the height of the ramp using the equation as shown below: \[\begin{align} & {{a}^{2}}+{{b}^{2}}={{c}^{2}} \\ & {{5}^{2}}+{{b}^{2}}={{6}^{2}} \\ & 25+{{b}^{2}}=36 \\ & {{b}^{2}}=36-25 \end{align}\] \[\begin{align} & {{b}^{2}}=11 \\ & b=\sqrt{11} \\ & b=3.3 \end{align}\] It is required to convert 3.3 m to feet. For conversion, meter is multiplied by 3.28 ft as shown below: \[\begin{align} & \text{1 m}=\text{3}\text{.28 ft} \\ & \text{3}\text{.3 m}=\text{3}\text{.3 m}\times \text{3}\text{.28 ft} \\ & =\text{10}\text{.824} \\ & \approx \text{10}\text{.8 ft} \end{align}\] The height of the ramp for bike competition seems unrealistic as the value is high to jump off for riders. Hence, option stating \[3.3\text{ m}\]expresses the ramp’s height. The height of the ramp is\[10.8\ \text{ft}\]. No, it does not seems to be realistic. (b) Compute the height of the ramp to nearest hundredths of the meter using the equation as shown below: \[\begin{align} & {{a}^{2}}+{{b}^{2}}={{c}^{2}} \\ & {{5}^{2}}+{{b}^{2}}={{6}^{2}} \\ & 25+{{b}^{2}}=36 \\ & {{b}^{2}}=36-25 \end{align}\] \[\begin{align} & {{b}^{2}}=11 \\ & b=\sqrt{11} \\ & =3.3166 \\ & \approx 3.3\text{ m} \end{align}\] It is required to convert 3.32m to cm. For conversion m is multiplied by 100 as shown below: \[\begin{align} & 3.32\text{ m}=3.32\times 100\text{ cm} \\ & =332\text{ cm} \end{align}\] It is required to convert 3.32m to inches to the nearest half inch. For conversion m is multiplied by 39.37 as shown below: \[\begin{align} & \text{3}\text{.32m}=\text{3}\text{.32 }\!\!\times\!\!\text{ 39}\text{.37 inches} \\ & =\text{130}\text{.708 inches} \\ & \text{nearest to half inch}\approx \text{130}\text{.70 in}\text{.} \end{align}\] Hence, the height of the ramp to the nearest hundredth of a meter is\[3.3\text{ m}\]. The difference in cm is\[2\text{ cm}\]. Height of the ramp in nearest half inches is \[130.70\text{ in}\text{.}\]No, the carpenter would not likely to make the error in measuring the exact inches with a tape measure. (c) It is required to convert 6 m to feet. For conversion, meter is multiplied by 3.28 ft. Compute the value of 6 m into feet as shown below: \[\begin{align} & \text{1 m}=\text{3}\text{.28 ft} \\ & \text{6 m}=\text{6}\times \text{3}\text{.28 ft} \\ & =\text{19}\text{.68 ft} \\ & \text{nearest tenth}=\text{19}\text{.7 ft} \end{align}\] The value of 6 m board in feet is\[19.7\text{ ft}\]. The board with this measurement was used to build the garden lawn. Hence, the value of 6 m board in feet is\[19.7\text{ ft}\] and the board of this length was there in the Depot 3 months ago.