Dora the Explorer must solve a right triangle, ΔABC where ∠C = 90° , a = 5 cm and b = 12 cm. She plans to use trigonometry and SOHCAHTOA to find the length of the hypotenuse. Why will Dora NOT be able to get an answer using this strategy ?

Question

Dora the Explorer must solve a right triangle, ΔABC  where  ∠C  =  90°  ,  a  =  5 cm  and  b  =  12 cm.  She plans to use trigonometry and SOHCAHTOA to find the length of the hypotenuse.  Why will Dora NOT be able to get an answer using this strategy ?

mathhelper · Accepted Answer

She would need to know either angle A or angle B,
but....
since she is an explorer, she would be somewhat educated and know that
c^2 = a^2 + b^2 applies and
c^2 = 5^2 + 12^2 = 169
c = √169 = 13

(she would also be familiar with the ratios of simple right-angled triangles such as the 3-4-5 or the 5-12-13 triangles)